Final Program and Abstracts 2015

Sponsored by the SIAM Activity Group on Dynamical Systems

The SIAM Activity Group on Dynamical Systems provides a forum for the exchange of ideas and information between mathematicians and applied scientists whose work involves dynamical systems. The goal of this group is to facilitate the development and application of new theory and methods of dynamical systems. The techniques in this area are making major contributions in many areas, including biology, nonlinear optics, fluids, chemistry, and mechanics. This activity group supports the web portal DSWeb, sponsors special sessions at SIAM meetings, organizes a biennial conference, and awards biennial prizes—the Jürgen Moser Lecture, J. D. Crawford Prize, and the Red Sock Award. The activity group also sponsors the DSWeb Student Competition for tutorials on dynamical systems and its applications written by graduate and undergraduate students and recent graduates. Members of SIAG/DS receive a complimentary subscription to the all- electronic, multimedia SIAM Journal on Applied Dynamical Systems.

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Table of Contents SIAM Registration Desk Child Care The SIAM registration desk is located in As a service to SIAM attendees, SIAM has Program-at-a-Glance...... Separate handout the Ballroom Foyer. It is open during the made arrangements for in-room child care. All sitters should be requested with at least General Information...... 2 following times: 48 hours notice. If you have not already made Saturday, May 16 Get-togethers...... 4 reservations for child care and would like to Featured Minisymposia...... 6 8:00 AM - 8:00 PM inquire about availability, please contact Camp Snowbird at (801)933-2256, or e-mail the Minitutorials...... 8 camp at [email protected]. Invited Plenary Presentations...... 9 Sunday, May 17 Prize and Special Lecture...... 11 8:00 AM - 5:00 PM Program Schedule...... 15 Corporate Members Poster Sessions...... 57 & 71 Monday, May 18 and Affiliates Abstracts...... 87 8:00 AM - 6:30 PM SIAM corporate members provide their Speaker and Organizer Index...... 233 employees with knowledge about, access Tuesday, May 19 to, and contacts in the applied mathematics Conference Budget.... Inside Back Cover and computational sciences community Hotel Meeting Room Map.... Back Cover 8:00 AM - 4:30 PM through their membership benefits. Corporate membership is more than just a bundle of tangible products and services; it is an Wednesday, May 20 expression of support for SIAM and its Organizing Committee 8:00 AM - 4:30 PM programs. SIAM is pleased to acknowledge its corporate members and sponsors. In Co-Chairs recognition of their support, non-member Thursday, May 21 Lora Billings attendees who are employed by the following Montclair State University, USA 8:00 AM - 4:45 PM organizations are entitled to the SIAM member registration rate.

Panayotis Kevrekidis University of Massachusetts Amherst, USA Hotel Address Corporate Institutional Snowbird Ski and Summer Resort 9320 S. Cliff Lodge Drive Members The Aerospace Corporation Organizing Committee Snowbird, UT 84092-9000 USA Air Force Office of Scientific Research Chiara Daraio Hotel web address: Aramco Services Company ETH Zürich, Switzerland http://www.snowbird.com/ AT&T Laboratories - Research Michelle Girvan University of Maryland, USA Bechtel Marine Propulsion Laboratory The Boeing Company Jan Medlock Hotel Telephone Number Oregon State University, USA To reach an attendee or leave a message, call CEA/DAM +1-801-742-2222. If the attendee is a hotel Department of National Defence (DND/CSEC) Igor Mezic guest, the hotel operator can connect you University of California, Santa Barbara, USA DSTO- Defence Science and Technology with the attendee’s room. Organisation Louis M. Pecora US Naval Research Laboratory, USA ExxonMobil Upstream Research Anthony Roberts Hotel Check-in Hewlett-Packard University of Adelaide, Australia and Check-out Times IBM Corporation Björn Sandstede Check-in time is 4:00 PM and check-out IDA Center for Communications Research, La Brown University, USA time is 11:00 AM. Jolla Mary Silber IDA Center for Communications Research, Northwestern University, USA Princeton Institute for Computational and Experimental Michael J. Ward Research in Mathematics (ICERM) University of British Columbia, Canada Institute for Defense Analyses, Center for Computing Sciences Lawrence Berkeley National Laboratory 2015 SIAM Conference on Applications of Dynamical Systems 3

Lockheed Martin Leading the applied Standard Audio/Visual Los Alamos National Laboratory mathematics community … Set-Up in Meeting Rooms Mathematical Sciences Research Institute Join SIAM and save! SIAM does not provide computers for Max-Planck-Institute for Dynamics of any speaker. When giving an electronic Complex Technical Systems presentation, speakers must provide their own SIAM members save up to $130 on full computers. SIAM is not responsible for the Mentor Graphics registration for the 2015 SIAM Conference safety and security of speakers’ computers. National Institute of Standards and on Dynamical Systems (DS15)! Join your Technology (NIST) peers in supporting the premier professional The Plenary Session Room will have two society for applied mathematicians and (2) screens, one (1) data projector and one National Security Agency (DIRNSA) computational scientists. SIAM members (1) overhead projector. The data projectors Oak Ridge National Laboratory, managed by receive subscriptions to SIAM Review, support VGA connections only. Presenters UT-Battelle for the Department of Energy SIAM News and SIAM Unwrapped, and requiring an HDMI or alternate connection Sandia National Laboratories enjoy substantial discounts on SIAM books, must provide their own adaptor. journal subscriptions, and conference Schlumberger-Doll Research All other concurrent/breakout rooms will have registrations. one (1) screen and one (1) data projector. The Tech X Corporation If you are not a SIAM member and paid the data projectors support VGA connections U.S. Army Corps of Engineers, Engineer Non-Member or Non-Member only. Presenters requiring an HDMI or Research and Development Center Mini Speaker/Organizer rate to attend the alternate connection must provide their own United States Department of Energy conference, you can apply the difference adaptor. between what you paid and what a member If you have questions regarding availability would have paid ($130 for a Non-Member of equipment in the meeting room of your List current March 2015. and $65 for a Non-Member Mini Speaker/ presentation, please see a SIAM staff member Organizer) towards a SIAM membership. at the registration desk. Contact SIAM Customer Service for details Funding Agencies or join at the conference registration desk. If you are a SIAM member, it only costs SIAM and the Conference Organizing Internet Access $10 to join the SIAM Activity Group on Committee wish to extend their thanks and Complimentary wireless Internet access Dynamical Systems (SIAG/DS). As a appreciation to the U.S. National Science will be available in the guest rooms and SIAG/DS member, you are eligible for an Foundation and the U.S. Department of public areas of the Cliff Lodge, the Lodge additional $10 discount on this conference, Energy for their support of this conference. at Snowbird, and the Inn. Additionally, so if you paid the SIAM member rate to complimentary wireless Internet access will attend the conference, you might be eligible be available in the meeting space of the Cliff for a free SIAG/DS membership. Check at Lodge. the registration desk. Email stations will also be available during Free Student Memberships are available to registration hours. students who attend an institution that is an Academic Member of SIAM, are members of Student Chapters of SIAM, or are nominated by a Regular Member of SIAM. Registration Fee Includes Join onsite at the registration desk, go to • Admission to all technical sessions www.siam.org/joinsiam to join online or • Business Meeting (open to SIAG/DS download an application form, or contact members) SIAM Customer Service: • Coffee breaks daily Telephone: +1-215-382-9800 (worldwide); • Poster Sessions and Dessert Receptions or 800-447-7426 (U.S. and Canada only) • Room set-ups and audio/visual Fax: +1-215-386-7999 equipment E-mail: [email protected] • Welcome Reception Postal mail: Society for Industrial and Applied Mathematics 3600 Market Street, 6th floor Philadelphia, PA 19104-2688 USA 4 2015 SIAM Conference on Applications of Dynamical Systems

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Featured Minisymposia Featured Minisymposia will include a selective group of talks that describe and promote recent significant advances in a theme deemed to be of high priority for current and near future research in Dynamical Systems and their Applications.

Sunday, May 17

2:00 PM – 4:00 PM

MS14: Applications of Algebraic Topology to Neuroscience Room: Ballroom I Organizers: Chad Giusti, University of Pennsylvania, USA Robert W. Ghrist, University of Pennsylvania, USA Danielle Bassett, University of Pennsylvania, USA

MS15: Data Assimilation in the Life Sciences Room: Ballroom II Organizers: Elizabeth M. Cherry, Cornell University, USA Timothy Sauer, George Mason University, USA

MS16: Data-Driven Modeling of Dynamical Processes in Spatially-Embedded Random Networks Room: Maybird Organizer: Gyorgy Korniss, Rensselaer Polytechnic Institute, USA

MS17: Stochastic Delayed Networks Room: Primrose A Organizer: Gabor Orosz, University of Michigan, Ann Arbor, USA

MS18: Localized Pattern Formation in Reaction-diffusion Equations Room: Primrose B Organizer: Arik Yochelis, Ben Gurion University Negev, Israel 2015 SIAM Conference on Applications of Dynamical Systems 7

Featured Minisymposia

Wednesday, May 20

4:00 PM - 6:00 PM

MS104: Non-Autonomous Instabilities Room: Ballroom I Organizer: Sebastian M. Wieczorek, University College Cork, Ireland

MS105: Random Walks, First Passage Time and Applications Room: Ballroom II Organizers: Theodore Kolokolnikov, Dalhousie University, Canada Sidney Redner, Santa Fe Institute, USA

MS106: Time-Delayed Feedback Room: Wasatch B Organizer: Andreas Amann, University College Cork, Ireland

MS107: Emerging Strategies for Stability Analysis of Electrical Power Grids Room: Maybird Organizers: Lewis G. Roberts, University of Bristol, United Kingdom Florian Dorfler, ETH Zürich, Switzerland

MS108: Invariant Manifolds Unravelling Complicated Dynamics Room: Primrose A Organizers: Stefanie Hittmeyer, University of Auckland, New Zealand Pablo Aguirre, Universidad Técnica Federico Santa María, Chile

MS109: Medical Applications Room: Primrose B Organizers: Dan D. Wilson, University of California, Santa Barbara, USA Jeff Moehlis, University of California, Santa Barbara, USA 8 2015 SIAM Conference on Applications of Dynamical Systems

Minitutorials

Sunday, May 17

2:00 PM - 4:00 PM MT1: Network Dynamics Room: Ballroom III Organizer: Louis M. Pecora, United States Naval Research Laboratory, USA

Wednesday, May 20

4:00 PM - 6:00 PM MT2: Stochastic Dynamics of Rare Events Room: Ballroom III Organizer: Eric Forgoston, Montclair State University, USA 2015 SIAM Conference on Applications of Dynamical Systems 9

Invited Plenary Speakers

** All Invited Plenary Presentations will take place in the Ballroom**

Sunday, May 17

11:45 AM - 12:30 PM IP1 Advances on the Control of Nonlinear Network Dynamics Adilson E. Motter, Northwestern University, USA

Monday, May 18

11:00 AM - 11:45 AM IP2 Mathematics of Crime Andrea L. Bertozzi, University of California, Los Angeles, USA

6:00 PM - 6:45 PM IP3 Filtering Partially Observed Chaotic Deterministic Dynamical Systems Andrew Stuart, University of Warwick, United Kingdom

Tuesday, May 19

11:00 AM - 11:45 AM IP4 Fields of Dreams: Modeling and Analysis of Large Scale Activity in the Brain Bard Ermentrout, University of Pittsburgh, USA 10 2015 SIAM Conference on Applications of Dynamical Systems

Invited Plenary Speakers

Wednesday, May 20

11:00 AM - 11:45 AM IP5 Cooperation, Cheating, and Collapse in Biological Populations Jeff Gore, Massachusetts Institute of Technology, USA

Thursday, May 21

11:15 AM - 12:00 PM IP6 Brain Control - It’s Not Just for Mad Scientists Jeff Moehlis, University of California, Santa Barbara, USA

4:15 PM - 5:00 PM IP7 The Robotic Scientist: Distilling Natural Laws from Raw Data, from Robotics to Biology and Physics Hod Lipson, Cornell University, USA 2015 SIAM Conference on Applications of Dynamical Systems 11

Prize Presentation and Special Lecture **The Prize Presentation and Special Lecture will take place in the Ballroom.**

SIAM Activity Group on Dynamical Systems Prizes

Sunday, May 17

8:00 PM - 8:15 PM Prize Presentations - Jürgen Moser and J. D. Crawford

J. D. Crawford Prize Recipient Florin Diacu, University of Victoria, Canada

Jürgen Moser Lecturer John Guckenheimer, Cornell University, USA

8:15 PM - 9:00 PM Jürgen Moser Lecture: Dynamics and Data John Guckenheimer, Cornell University, USA 12 2015 SIAM Conference on Applications of Dynamical Systems

SIAM Activity Group on Dynamical Systems (SIAG/DS)

www.siam.org/activity/ds A GREAT WAY TO GET INVOLVED! Collaborate and interact with mathematicians and applied scientists whose work involves dynamical systems.

ACTIVITIES INCLUDE: 2015 • DSWeb portal ► • Special sessions at SIAM meetings ► • Biennial conference ► • Jürgen Moser Lecture ► • J. D. Crawford Prize ► • Red Sock Award

BENEFITS OF SIAG/DS MEMBERSHIP: • Listing in the SIAG’s online membership directory • Additional $10 discount on registration at the SIAM Conference on Applied Dynamical Systems (excludes students) • Dynamical Systems Magazine • Subscription to SIAM Journal on Applied Dynamical Systems ► • Electronic communications about recent developments in your specialty ► • Eligibility for candidacy for SIAG/DS office ► • Participation in the selection of SIAG/DS officers

ELIGIBILITY: • Be a current SIAM member. COST: • $10 per year • Student members can join 2 activity groups for free! 2014-15 SIAG/DS OFFICERS Chair: Timothy D Sauer, George Mason University Vice Chair: Vivi Rottschafer, Universiteit Leiden Program Director: Lora Billings, Montclair State University Secretary and DS Magazine Chief Editor: Elizabeth Cherry, Rochester Institute of Technology DSWeb Portal Editor-in-Chief: Peter van Heijster, Queensland University of Technology

TO JOIN:

SIAG/DS: my.siam.org/forms/join_siag.htm SIAM: www.siam.org/joinsiam 2015 SIAM Conference on Applications of Dynamical Systems 13 14 2015 SIAM Conference on Applications of Dynamical Systems 2015 SIAM Conference on Applications of Dynamical Systems 15

Final Program

2015 16 2015 SIAM Conference on Applications of Dynamical Systems

Saturday, May 16 Sunday, May 17 Sunday, May 17 Registration MS1 Patterns in Partial Differential Registration 8:00 AM-5:00 PM Equations - Part I of II 8:00 AM-8:00 PM Room:Ballroom Foyer 9:00 AM-11:00 AM Room:Ballroom Foyer Room:Ballroom I SIAM Workshop on Network For Part 2 see MS19 Science (May 16-17 -- Patterns play an important role in the SIAM Workshop on Network separate fees apply) dynamics of many dissipative and dispersive Science (May 16-17 -- PDEs, posed on large or unbounded 8:30 AM-6:00 PM separate fees apply) domains. This minisymposium will feature Room:Cottonwood Room - Snowbird contributions that investigate intrinsically multi-dimensional aspects of the dynamics of 9:00 AM-8:30 PM Center patterns, including their existence, stability, Room:Cottonwood Room - Snowbird instability, slow evolution, and interaction. Center Examples include interfaces between patterned and un-patterned state, point defects or vortices, and line defects. We expect to Welcome Reception bring together researchers with a variety of backgrounds, employing a variety of 6:00 PM-8:00 PM techniques, such as diffusive and dispersive stability estimates, energy methods from the Room:Ballroom calculus of variations, or spatial dynamics and bifurcation methods. Organizer: Keith Promislow Michigan State University, USA Organizer: Noa Kraitzman Michigan State University, USA 9:00-9:25 Bifurcation and Competitive Evolution of Network Morphologies in the Strong Functionalized Cahn- Hilliard Equation Noa Kraitzman, Michigan State University, USA 9:30-9:55 Nonlinearity Saturation as a Singular Perturbation of the Nonlinear Schrödinger Equation Karl Glasner, University of Arizona, USA 10:00-10:25 Dark-Bright, Dark-Dark, Vortex-Bright and Other Multi- Component NLS Beasts: Theory and Recent Applications Panayotis Kevrekidis, University of Massachusetts, USA 10:30-10:55 Nonlinear Stability of Source Defects Bjorn Sandstede, Brown University, USA 2015 SIAM Conference on Applications of Dynamical Systems 17

Sunday, May 17 Sunday, May 17 Sunday, May 17 MS2 MS3 MS4 Dynamics of Boolean Ocean-in-the-loop: Towards Dynamics of Rigid Bodies Switching Networks Real-Time Monitoring in and Fluids 9:00 AM-11:00 AM Geophysical Flows - 9:00 AM-11:00 AM Part I of II Room:Ballroom II Room:Magpie A Modeling complex systems in general, 9:00 AM-11:00 AM This interdisciplinary minisymposium will and gene regulation in particular, presents Room:Ballroom III address mathematical methods used in the particular challenges. The challenges rigid body mechanics, fluid mechanics, and For Part 2 see MS21 include the large size of biologically fluid-structure interaction. The lectures will Improved modeling and prediction of fluid relevant gene networks and the ability to include topics on dynamics of nonholonomic dynamics is needed to better understand parameterize ODE models. The available systems, coupled rigid body and fluid ocean and atmospheric transport along with data are often only qualitative and therefore motion, links between nonholonomic associated applications including contaminant it is not clear how to compare them to a mechanics and fluids, and a geometric dispersion, environmental modeling, and precise solutions of an ODE system. An approach to numerical fluid dynamics. underwater acoustic propagation. Major attractive answer to these challenges is the The unifying idea of this minisymposium recent advances in closed-loop adaptive framework of switching systems, which is the representation of the rigid body and sampling, Lagrangian data assimilation, combine continuous time evolution of an fluid dynamics in the form of of the Euler- uncertainty quantification, and phase ODE system with discrete, or Boolean Poincare (resp., Lie-Poisson) equations in the space transport are providing improved quantization of the phase space. The Lagrangian (resp., Hamiltonian) setting. understanding of transport phenomena. minisymposium will bring together the The purpose of this minisymposium is to Organizer: Dmitry Zenkov leading researchers in the area to provide an expose the audience to recent progress and North Carolina State University, USA overview of this very active field. developments, as well as to bring together Organizer: Scott D. Kelly Organizer: Tomas Gedeon researchers developing new mathematical University of Illinois at Urbana- Montana State University, USA methods and applications for use in Champaign, USA Organizer: Roderick Edwards understanding flow transport. 9:00-9:25 The Lie-Dirac Reduction for Organizer: Eric Forgoston University of Victoria, Canada Nonholonomic Systems on Semidirect 9:00-9:25 Database for Switching Montclair State University, USA Products Networks As a Tool for Study of Gene Organizer: Ani Hsieh Hiroaki Yoshimura, Waseda University, Networks Drexel University, USA Japan; François Gay-Balmaz, Ecole Tomas Gedeon, Montana State University, Normale Superieure de Paris, France 9:00-9:25 Tracking of Geophysical USA Flows by Robot Teams: An 9:30-9:55 Discretization of Hamiltonian 9:30-9:55 Gene Network Models Experimental Approach Incompressible Fluids Including mRNA and Protein Ani Hsieh, Dhanushka Kularatne, and Gemma Mason, California Institute of Dynamics Dennis Larkin, Drexel University, USA; Technology, USA; Christian Lessig, Roderick Edwards, University of Victoria, Eric Forgoston, Montclair State University, Technische Universität Berlin, Germany; Canada USA; Philip Yecko, Cooper Union, USA Mathieu Desbrun, California Institute of 10:00-10:25 Evolution of Gene 9:30-9:55 Controlled Lagrangian Technology, USA Networks Prediction Using An Ensemble of Flow 10:00-10:25 Constrained Motion Leon Glass, McGill University, Canada Models of Point Vortices Interacting 10:30-10:55 Dynamics of Fumin Zhang, Georgia Institute of Dynamically with Rigid Bodies in Autonomous Boolean Networks Technology, USA Ideal Flow and Scott Kelly, Otti D’Huys and Nicholas D. Haynes, 10:00-10:25 Conditional Statistics with Michael Fairchild Duke University, USA; Miguel C. Lagrangian Coherent Structures University of North Carolina, Charlotte, USA Soriano and Ingo Fischer, Universitat Wenbo Tang and Phillip Walker, Arizona de les Illes Balears, Spain; Daniel J. State University, USA 10:30-10:55 The Poincare-Hopf Gauthier, Duke University, USA Theorem in Nonholonomic 10:30-10:55 Controlling Long-Term Mechanics Spatial Distributions of Autonomous Vehicles in Stochastic Flow Oscar Fernandez, Wellesley College, Environments USA; Anthony M. Bloch, University of Michigan, USA; Dmitry Zenkov, North Christoffer R. Heckman, University of Carolina State University, USA Colorado Boulder, USA; Ani Hsieh, Drexel University, USA; Ira B. Schwartz, Naval Research Laboratory, USA 18 2015 SIAM Conference on Applications of Dynamical Systems

Sunday, May 17 Sunday, May 17 Sunday, May 17 MS7 MS8 MS9 The Dynamics and Wave-turbulence Interactions Dynamics on Networks Computation of Neuronal in Geophysical and and Network Topology in Networks Astrophysical Fluid Dynamics Ecology and Epidemiology 9:00 AM-11:00 AM 9:00 AM-11:00 AM 9:00 AM-11:00 AM Room:Wasatch B Room:Maybird Room:Superior A The dynamics of neuronal networks provide The interaction of waves and turbulence is a The spread of pathogens in population rich information regarding the nature of topic of fundamental importance in geophysical networks or of invasive species in fragmented computation and information encoding in and astrophysical fluid dynamics, where wave landscapes give rise to dynamical systems the brain. This minisymposium explores dynamics result from density stratification, defined on networks. The topology of the recent work in the modeling of neuronal rotation, magnetism, and compressibility. The network has implications for the dynamics, dynamics, emphasizing implications on interactions of wave dynamics with turbulence constraining, for example, if spread through sensory processing and network connectivity. can have significant implications, transferring the network is wave-like or if new clusters The speakers will draw particular attention to energy over long distances or across scales, can form at long distances from old ones. new mathematical advances in characterizing and impacting the formation and evolution New topological tools such as persistent the structure-function relationship for of coherent structures. This minisymposium topology developed for studying data sets complex neuronal networks and techniques brings together researchers to present recent such as large point clouds or networks allow for understanding the biophysical processes results in wave-turbulence interaction in both for new insights into dynamics on networks. underlying network dynamics. geophysical and astrophysical settings. Topics in the minisymposium include spatially embedded contagion networks and Organizer: Ian Grooms Organizer: Victor Barranca network-mediated dynamical systems models New York University, USA New York University, USA in ecology and epidemiology, all informed by Organizer: Douglas Zhou Organizer: Jared P. Whitehead the underlying network topology. Shanghai Jiao Tong University, China Brigham Young University, USA Organizer: Christopher Strickland 9:00-9:25 Reconstruction of Structural 9:00-9:25 Internal Wave Generation by University of North Carolina at Chapel Connectivity in Neuronal Networks Convection Hill, USA Using Compressive Sensing of Network Daniel Lecoanet, University of California, Organizer: Patrick Shipman Dynamics Berkeley, USA; Keaton Burns, Colorado State University, USA Victor Barranca, New York University, Massachusetts Institute of Technology, USA; Douglas Zhou, Shanghai Jiao Tong USA; Geoffrey M. Vasil, University of 9:00-9:25 Network Spread and Control University, China; David Cai, Shanghai Sydney, Australia; Eliot Quataert, University of Invasive Species and Infectious Jiao Tong University, China and Courant of California, Berkeley, USA; Benjamin Diseases Institute of Mathematical Sciences, New Brown, University of Colorado Boulder, Christopher Strickland, University of York University, USA USA; Jeffrey Oishi, Farmingdale State North Carolina at Chapel Hill, USA; College, USA Patrick Shipman, Colorado State 9:30-9:55 Theoretical Modeling of University, USA Neuronal Dendritic Integration 9:30-9:55 Interaction of Inertial Songting Li, Courant Institute of Oscillations with a Geostrophic Flow 9:30-9:55 Topological Data Analysis Mathematical Sciences, New York Jim Thomas, Courant Institute of for and with Contagions on Networks University, USA; Douglas Zhou, Shanghai Mathematical Sciences, New York Dane Taylor, University of North Carolina Jiao Tong University, China; David Cai, University, USA; Shafer Smith, Courant at Chapel Hill, USA; Florian Klimm, Courant Institute of Mathematical Sciences, Institute, Center for Atmosphere Ocean Humboldt University Berlin, Germany; New York University, USA Science, USA; Oliver Buhler, Courant Heather Harrington, University of Oxford, Institute of Mathematical Sciences, New United Kingdom; Miroslav Kramar 10:00-10:25 Topology Reconstruction York University, USA and Konstantin Mischaikow, Rutgers of Neuronal Networks University, USA; Mason A. Porter, , Yanyang Xiao, Yaoyu 10:00-10:25 Investigation of Boussinesq Douglas Zhou University of Oxford, United Kingdom; Zhang, and Zhiqin Xu, Shanghai Jiao Tong non-linear Interactions Using Peter J. Mucha, University of North University, China; David Cai, Shanghai Intermediate Models Carolina at Chapel Hill, USA Jiao Tong University, China and Courant Gerardo Hernandez-Duenas, National Institute of Mathematical Sciences, New University of Mexico, Mexico; Leslie Smith, York University, USA University of Wisconsin, USA; Samuel Stechmann, University of Wisconsin, 10:30-10:55 Functional Connectomics Madison, USA from Data: Constructing Probabilistic Graphical Models for Neuronal 10:30-10:55 Interactions Between Near- Networks Inertial Waves and Turbulence in the Ocean Eli Shlizeman, University of Washington, continued on next page USA Jacques Vanneste, University of Edinburgh, United Kingdom 2015 SIAM Conference on Applications of Dynamical Systems 19

10:00-10:25 Local Inference of Gene Sunday, May 17 Sunday, May 17 Regulatory Networks from Time Series Data MS10 MS11 Francis C. Motta, Kevin McGoff, Anastasia Deckard, Xin Guo Guo, Tina Kelliher, Dynamics Modeling with Multiscale Models to Adam Leman, Steve Haase, and John Transformations Between Understand the Social and Harer, Duke University, USA Partial- and Delay Physical World - Part I of II 10:30-10:55 Patterns in Discrete Differential Equations Ecological Dynamical Systems 9:00 AM-11:00 AM Revealed Through Persistent 9:00 AM-11:00 AM Room:White Pine Homology Room:Superior B For Part 2 see MS29 Rachel Neville, Colorado State University, The scientific community has developed a rich USA Travelling wave solutions of the governing partial differential equations (PDEs) of and diverse library of mathematical models distributed parameter systems often lead to capable of capturing complex processes and the transformation of the infinite dimensional interactions over a broad range of scales in problem to a corresponding system of space and time. In this session, we feature delay differential equations (DDEs). The a variety of researchers exploring the transformations from DDEs to PDEs may application of mathematical models to the also be useful for analyzing certain classes social and physical world. The topics of this of dynamical systems. The lectures give a session cover several scales, from interacting spectrum of these transformations revealing particles to population models to PDEs, and the intricate dynamical properties of these include both stochastic and deterministic systems, like the peculiar stability properties models. Talks will address applications such of periodic retarded systems, neutral systems as earthquakes, swimming microorganisms, with multiple delays, tau-nonstabilizable and human crowd dynamics. systems, delayed boundary value problems Organizer: Alethea Barbaro and variable delay systems, which are Case Western Reserve University, USA often linked to models of dynamic contact problems. Organizer: Brittany Erickson Portland State University, USA Organizer: Gabor Stepan Budapest University of Technology and 9:00-9:25 Phase Transitions in Models Economics, Hungary for Social Dynamics Alethea Barbaro, Case Western Reserve 9:00-9:25 What Is Wrong with Non- University, USA Smooth Mechanics and How Memory Effects Can Fix It? 9:30-9:55 A Center Manifold and Robert Szalai, University of Bristol, United Complex Phases for a Large Number Kingdom of Interacting Particles Bjorn Birnir, University of California, Santa 9:30-9:55 Differential Equations with Barbara, USA; Luis Bonilla, Universidad Variable Delay and Their Connection Carlos III de Madrid, Spain; Jorge Cornejo- to Partial Differential Equations Donoso, University of California, Santa Gunter Radons, Andreas Otto, and Barbara, USA David Mueller, Chemnitz University of Technology, Germany 10:00-10:25 Mathematical Challenges in Ground State Formation of Isotropic 10:00-10:25 Stability Analysis of PDEs and Anisotropic Interaction with Two Spatial Dimensions Using David T. Uminsky, University of San Lyapunov Methods and SOS Francisco, USA Evgeny Meyer and Matthew Peet, Arizona State University, USA 10:30-10:55 Modeling Earthquake Cycles on Faults Separating Variable 10:30-10:55 Delayed Boundary Materials Conditions in Control of Continua Brittany Erickson, Portland State University, Gabor Stepan, Budapest University of USA Technology and Economics, Hungary; Li Zhang, Nanjing University of Aeronautics and Astronautics, China 20 2015 SIAM Conference on Applications of Dynamical Systems

Sunday, May 17 Sunday, May 17 Sunday, May 17 MS12 MS13 MS23 Network Synchronization in Dynamics of High Oscillations in Systems with Mechanical Systems and Dimensional Stochastic Relays Beyond - Part I of II Models 9:00 AM-11:00 AM 9:00 AM-11:00 AM 9:00 AM-11:00 AM Room:Magpie B Room:Primrose A Room:Primrose B This minisymposium aims to strengthen the For Part 2 see MS30 High dimensional models can arise from link between the theory and applications This minisymposium focuses on the role of spatially extended systems or systems with of systems with relay nonlinearities. A synchronization, coordination, and dynamical large numbers of interacting units (i.e. atoms, particular attention will be given to those consensus in mechanical systems and beyond. neurons, people, ect.). The observed global theoretical tools that allow designing Examples range from bridges and mechanical behavior of these systems can be characterized closed orbits in real life applications. Both pendula to self-organizing networks of through the analysis and simulation of large local bifurcation technique and available moving agents, with application in robotics dimensional differential equation (SDE) and global methods will be addressed. On the and animal behavior. This minisymposium stochastic partial differential equation (SPDE) modelling side, the minisymposium covers aims at various theoretical and experimental models. We look at applications including the relay systems described by discontinuous aspects of synchrony-induced phenomena pattern formation, ferromagnets, molecular differential equations as well as functional- and their control and brings together applied dynamics, and viscoelastic fluids. differential equations with hysteresis operators. mathematicians and mechanical engineers. Organizer: Katherine Newhall Organizer: Igor Belykh University of North Carolina at Chapel Organizer: Dmitry Rachinskiy Georgia State University, USA Hill, USA University of Texas at Dallas, USA Organizer: Maurizio Porfiri 9:00-9:25 Low-Damping Transition 9:00-9:25 Population Dynamics with Polytechnic Institute of New York Times in a Ferromagnetic Model the Preisach Operator Dmitry Rachinskiy, University of Texas at University, USA System Katherine Newhall, University of North Dallas, USA 9:00-9:25 Wind-Induced Synchrony Carolina at Chapel Hill, USA Causes the Instability of a Bridge: 9:30-9:55 Self-Oscillations Via Two- When Millennium Meets Tacoma 9:30-9:55 Tipping and Warning Signs Relay Controller: Design, Analysis, and Applications Igor Belykh and Russell Jeter, Georgia for Patterns and Propagation Failure in State University, USA; Vladimir Belykh, SPDEs Luis T. Aguilar, Instituto Politécnico Lobachevsky State University of Nizhny Christian Kuehn, Vienna University of Nacional, Mexico; Igor Boiko, The Novgorod, Russia Technology, Austria; Karna V. Gowda, Petroleum Institute of Abu Dhabi, United Northwestern University, USA Arab Emirates; Leonid Fridman and Rafael 9:30-9:55 Versatile Vibrations: Partially Iriarte, Universidad Nacional Autonoma de Synchronized States in Mechanical 10:00-10:25 Fluctuating Mexico, Mexico Systems from Microns to Kilometers Hydrodynamics of Microparticles in 10:00-10:25 Periodic Solutions in Daniel Abrams, Northwestern University, Viscoelastic Fluids Dynamical Systems with Relay: USA Scott McKinley, University of Florida, USA Existence, Stability, Bifurcations 10:00-10:25 Synchronization over 10:30-10:55 Stochastic Boundary Pavel Gurevich, Free University of Berlin, Networks Inspired by Echolocating Conditions for Molecular Dynamics: Germany Bats From Crystal to Melt Subhradeep Roy and Nicole Abaid, Virginia Gregory J. Herschlag, Duke University, 10:30-10:55 Reaction-Diffusion Equations with Discontinuous Relay Tech, USA USA; Sorin Mitran, University of North Carolina, Chapel Hill, USA Nonlinearity 10:30-10:55 Network Graph Can Sergey Tikhomirov, St. Petersburg State Promote Faster Consensus Reach University, Russia; Pavel Gurevich, Free Despite Large Inter-Agent Delays University of Berlin, Germany Min Hyong Koh and Rifat Sipahi, Northeastern University, USA 2015 SIAM Conference on Applications of Dynamical Systems 21

Sunday, May 17 Sunday, May 17 Sunday, May 17 MS116 Coffee Break IP1 Torus Canards in 11:00 AM-11:30 AM Advances on the Control Applications Room:Golden Cliff of Nonlinear Network 9:00 AM-11:00 AM Dynamics 11:45 AM-12:30 PM Room:Wasatch A Welcome Remarks Torus canards arise in slow/fast systems in Room:Ballroom 11:30 AM-11:45 AM which the fast subsystem contains families Chair: Louis M. Pecora, Naval of attracting and repelling limit cycles that Room:Ballroom Research Laboratory, USA meet in a saddle-node bifurcation of limit cycles. In models of neuronal systems, the An increasing number of complex systems transition from spiking (rapid firing of the are now modeled as networks of coupled membrane potential) to bursting (alternating dynamical entities. Nonlinearity and intervals of spiking and quiescence) can high-dimensionality are hallmarks of occur via torus canards. Characterised by the dynamics of such networks but have long excursions near the repelling manifold generally been regarded as obstacles to of limit cycles, torus canards are the higher- control. In this talk, I will discuss recent dimensional analogue of classical canards. advances on mathematical and computational This minisymposium consists of case studies approaches to control high-dimensional that illustrate how torus canards give rise nonlinear network dynamics under general to rich dynamical phenomena in various constraints on the admissible interventions. I applications. will present applications to the stabilization of power grids, identification of new Organizer: Kerry-Lyn Roberts therapeutic targets, mitigation of extinctions University of Sydney, Australia in food webs, and control of systemic Organizer: Theodore Vo failures in socio-economic systems. These Boston University, USA examples will illustrate the potential and limitations of existing methods to address 9:00-9:25 The Interaction Between a broad class of problems, ranging from Classical Canards and Torus Canards cascade control and transient stability to Theodore Vo, Boston University, USA network reprogramming in general. 9:30-9:55 Averaging and Generic Adilson E. Motter Torus Canards Northwestern University, USA Kerry-Lyn Roberts, University of Sydney, Australia 10:00-10:25 Averaging and Kam Theory in Torus Canards Albert Granados, INRIA, France Lunch Break 10:30-10:55 Torus Canard Breakdown 12:30 PM-2:00 PM Andrey Shilnikov, Georgia State University, Attendees on their own USA; Alexander Neiman, Ohio University, USA 22 2015 SIAM Conference on Applications of Dynamical Systems

Sunday, May 17 Sunday, May 17 Sunday, May 17 MT1 MS14 MS15 Network Dynamics Featured Minisymposium: Featured Minisymposium: 2:00 PM-4:00 PM Applications of Algebraic Data Assimilation in the Life Room:Ballroom III Topology to Neuroscience Sciences Chair: Louis M. Pecora, Naval Research 2:00 PM-4:00 PM 2:00 PM-4:00 PM Laboratory, USA Room:Ballroom I Room:Ballroom II Over the last decade or more analysis of The varied subjects of study in neuroscience, Assimilation of data with models of networks has developed into a topic all its from brain network dynamics to clinical physical and biological processes is a crucial own in mathematics and many sciences diagnosis, provide an abundant source of component of modern scientific analysis. In (physics, biology, sociology, neuroscience, fundamentally non-linear problems which recent years, nonlinear versions of Kalman etc.). Many journals have sections for papers emerging tools in computational algebraic filtering have been developed, in addition on network analysis. This minitutorial will topology are well-suited to address. to methods that estimate model parameters present the audience with an overview of Conversely, these new applications call in parallel with the system state. This network science including useful techniques for the development of new theoretical minisymposium highlights the state of the and tools along with more abstract concepts. structure through which to interpret results art in applying these techniques to nonlinear The speakers will also comment on new ideas and form hypotheses. This minisymposium dynamical systems in the life sciences to gain and approaches that are beginning to surface. showcases some recent applications and the understanding from biological data. The talks From Structure to Dynamics in directions in which the theory is evolving to will illustrate the use of data assimilation to Complex Networks accommodate them. analyze the dynamics of several prototypical Michelle Girvan, University of Maryland, Organizer: Chad Giusti systems, such as cardiac tissue, hippocampal neurons and neural cultures. USA University of Pennsylvania, USA Organizer: Elizabeth M. Cherry Networks, Dynamics, and the Organizer: Robert W. Ghrist Cornell University, USA Ongoing Evolution University of Pennsylvania, USA Mason A. Porter, University of Oxford, Organizer: Timothy Sauer Organizer: Danielle Bassett United Kingdom George Mason University, USA University of Pennsylvania, USA 2:00-2:25 Intramural Forecasting 2:00-2:25 Topological Detection of Cardiac Dynamics Using Data of Structure in Neural Activity Assimilation Recordings Matthew J. Hoffman, Rochester Institute Chad Giusti, University of Pennsylvania, of Technology, USA; Elizabeth M. Cherry, USA; Carina Curto and Vladimir Itskov, Cornell University, USA Pennsylvania State University, USA 2:30-2:55 Reconstructing Dynamics of 2:30-2:55 An Algebro-Topological Unmodeled Variables Perspective on Hierarchical and Timothy Sauer, Modularity of Networks Franz Hamilton George Mason University, USA Kathryn Hess, École Polytechnique Fédérale de Lausanne, Switzerland 3:00-3:25 Modeling Excitable Dynamics of Cardiac Cells 3:00-3:25 The Topology of Fragile X , T.K. Shajahan, Jan Syndrome Sebastian Berg Schumann-Bischoff, Ulrich Parlitz, and David Romano, Stanford University School Stefan Luther, Max Planck Institute for of Medicine, USA Dynamics and Self-Organization, Germany 3:30-3:55 The Neural Ring: Using 3:30-3:55 Tracking Neuronal Algebraic Geometry to Analyze Dynamics During Seizures and Neural Codes Alzheimer’s Disease Nora Youngs, Harvey Mudd College, USA Ghanim Ullah, University of South Florida, USA 2015 SIAM Conference on Applications of Dynamical Systems 23

Sunday, May 17 Sunday, May 17 Sunday, May 17 MS16 MS17 MS18 Featured Minisymposium: Featured Minisymposium: Featured Minisymposium: Data-Driven Modeling Stochastic Delayed Localized Pattern Formation of Dynamical Processes Networks in Reaction-diffusion in Spatially-Embedded 2:00 PM-4:00 PM Equations Random Networks Room:Primrose A 2:00 PM-4:00 PM 2:00 PM-4:00 PM Complex systems of the 21st century may Room:Primrose B Room:Maybird exhibit rich dynamical behaviors due to Spatially localized states have recently brought complicated network structures, time delays Infrastructure, transportation, and brain to the spotlight of mathematical analysis and stochastic effects. Understanding the networks are embedded in strongly of nonlinear PDEs via analysis of models dynamics of such infinite dimensional heterogeneous spatial environments, posing exhibiting free energy and/or conservation. dynamical systems requires new approaches formidable challenges in understanding The purpose of this minisymposium is to and novel mathematical tools. This sections the vulnerability or “plasticity” of these generalize and discuss the state of the art in highlights the latest research result on systems. There exists a large gap between localized pattern formation theory through the the dynamics of networks where time some universal features of simplified reaction diffusion framework that is related delays arise due to finite-time information dynamical processes on non-spatial complex to applications across a range of problems propagation between the nodes and networks and their applicability to real-world in chemistry and biology. The focus will be stochasticity appears both in the state as well problems. This minisymposium will present devoted to recent theories and computations as in the time delays. Applications include recent progress by data-driven approaches in of spatially localized patterns that can result neural networks, gene regulatory networks, diverse areas. Topics will include the lack of from a number of different mechanisms, and connected vehicle systems. self-averaging and predictability of cascading such as sub-critical bifurcations, homoclinic failures in power grids, optimization in Organizer: Gabor Orosz snaking, singular perturbations and semi-strong smart grids, the applicability of scaling laws University of Michigan, Ann Arbor, USA interaction asymptotics. of human travel, and the impact of wiring 2:00-2:25 Dynamics with Organizer: Arik Yochelis constraints and weight-based heterogeneity in Stochastically Delayed Feedback: Ben Gurion University Negev, Israel the cortical networks. Designing Connected Vehicle 2:00-2:25 The Origin of Finite Pulse Organizer: Gyorgy Korniss Systems Trains: Homoclinic Snaking in Excitable Rensselaer Polytechnic Institute, USA Gabor Orosz and Wubing Qin, University Media of Michigan, Ann Arbor, USA 2:00-2:25 Cascading Failures and Arik Yochelis, Ben Gurion University Negev, Stochastic Methods for Mitigation 2:30-2:55 New Mechanisms for Israel; Edgar Knobloch, University of in Spatially-Embedded Random Patterns, Transitions, and Coherence California, Berkeley, USA Networks Resonance for Systems with Delayed 2:30-2:55 Homoclinic Snaking Near Gyorgy Korniss, Rensselaer Polytechnic Feedback a Codimension-two Turing-Hopf Institute, USA Rachel Kuske and Chia Lee, University Bifurcation Point of British Columbia, Canada; Vivi 2:30-2:55 Feasibility of Micro-Grid Justin C. Tzou, Dalhousie University, Canada; Rottschaefer, Leiden University, Adoptions in Spatially-Embedded Yiping Ma, University of Colorado Boulder, Netherlands Urban Networks USA; Alvin Bayliss, Bernard J Matkowsky, Marta Gonzalez, Massachusetts Institute of 3:00-3:25 Synchronization of Degrade- and Vladimir A. Volpert, Northwestern Technology, USA and-Fire Oscillations Via a Common University, USA Activator 3:00-3:25 Spatial Distribution of 3:00-3:25 Slow Dynamics of Localized William H. Mather, Virginia Tech, USA; Jeff Population and Scaling in Human Spot Patterns for Reaction-Diffusion Hasty and Lev S. Tsimring, University of Travel Systems on the Sphere California, San Diego, USA Zoltan Neda, Babes-Bolyai University, Philippe H. Trinh, Princeton University, USA; Romania; Geza Toth, Hungarian Central 3:30-3:55 On the Role of Stochastic Michael Ward, University of British Statistical Office, Hungary; Andras Delays in Gene Regulatory Networks Columbia, Canada Kovacs, Edutus College, Hungary; Istvan Marcella Gomez and Matthew Bennett, 3:30-3:55 Localised Solutions in a Non- Papp and Levente Varga, Babes-Bolyai Rice University, USA; Richard Murray, Conservative Cell Polarization Model University, Romania California Institute of Technology, USA Nicolas Verschueren Van Rees and Alan 3:30-3:55 The Brain in Space Champneys, University of Bristol, United Zoltan Toroczkai, University of Notre Kingdom Dame, USA; Maria Ercsey-Ravasz, Babes- Bolyai University, Romania; Kenneth Knoblauch and Henry Kennedy, Inserm, Coffee Break France 4:00 PM-4:30 PM Room:Golden Cliff 24 2015 SIAM Conference on Applications of Dynamical Systems

Sunday, May 17 Sunday, May 17 Sunday, May 17 CP1 CP2 CP3 Topics in Reaction-Diffusion Topics in Pattern Formation I Topics in Networks I Systems 4:30 PM-6:30 PM 4:30 PM-6:10 PM 4:30 PM-6:30 PM Room:Ballroom II Room:Ballroom III Room:Ballroom I Chair: Jose Morales Morales, INRIA Chair: Christian Bick, Rice University, Chair: Petrus van Heijster, Queensland Rhone, France USA University of Technology, Australia 4:30-4:45 Generalized Behavior of the 4:30-4:45 Analysis of Connected 4:30-4:45 Defect Solutions in Reaction- Two-phase System in (1+1) D Vehicle Networks with Nontrivial Diffusion Equations David A. Ekrut and Nicholas Cogan, Connectivity, a Modal Decomposition Approach Peter van Heijster, Queensland University Florida State University, USA Sergei S. Avedisov and Gabor Orosz, of Technology, Australia 4:50-5:05 Discrete Synchronization of University of Michigan, Ann Arbor, USA 4:50-5:05 Reaction-Diffusion Equations Massively Connected Systems Using with Spatially Distributed Hysteresis in Hierarchical Couplings 4:50-5:05 Phase Response Properties Higher Spatial Dimensions Camille Poignard, Université de Nice, of Collective Rhythms in Networks of Coupled Dynamical Systems Mark J. Curran, Free University of Berlin, Sophia Antipolis, France Hiroya Nakao and Sho Yasui, Tokyo Germany 5:10-5:25 Nonlinear Dynamics of Two- Institute of Technology, Japan 5:10-5:25 Spatio-Temporal Dynamics Colored Filaments of Heterogeneous Excitable Media Alexey Sukhinin and Alejandro Aceves, 5:10-5:25 Heterogeneities in Temporal Networks Emerging from Adaptive Thomas Lilienkamp, Ulrich Parlitz, and Southern Methodist University, USA Social Interactions Stefan Luther, Max Planck Institute for 5:30-5:45 Scaling and Robustness Takaaki Aoki, Kagawa University, Japan; Dynamics and Self-Organization, Germany of Two Component Morphogen Luis Rocha, Karolinska Institutet, Sweden; Patterning Systems 5:30-5:45 Existence of Periodic Thilo Gross, University of Bristol, United Solutions of the FitzHugh-Nagumo Md. Shahriar Karim, Purdue University, Kingdom Equations for An Explicit Range of the USA; Hans G. Othmer, University of Small Parameter Minnesota, USA; David Umulis, Purdue 5:30-5:45 Simulating the Dynamics of College Drinking Aleksander Czechowski and Piotr University, USA Ben G. Fitzpatrick, Jason Martinez, and Zgliczyński, Jagiellonian University, 5:50-6:05 Solitary Waves in the Elizabeth Polidan, Tempest Technologies Poland Excitable Discrete Burridge-Knopoff LLC, USA 5:50-6:05 Morse-Floer Homology for Model Travelling Waves in Reaction-Diffusion Jose Eduardo Morales Morales, 5:50-6:05 Integrating Hydrological and Equations Guillaume James, and Arnaud Tonnelier, Waterborne Disease Network Models Berry Bakker, Jan Bouwe Van Den Berg, INRIA Rhone, France Karly Jacobsen and Michael Kelly, The Ohio State University, USA; Faisal Hossain, and Robert van Der Vorst, VU University, 6:10-6:25 Aspects and Applications University of Washington, USA; Joseph H. Amsterdam, Netherlands of Generalized Synchronization Tien, The Ohio State University, USA 6:10-6:25 Low Dimensional Models Ulrich Parlitz, Max Planck Institute of Diffusion and Reaction in Stratified for Dynamics and Self-Organization, Micro Flows Germany Jason R. Picardo and Subramaniam Pushpavanam, Indian Institute of Technology Madras, India 2015 SIAM Conference on Applications of Dynamical Systems 25

Sunday, May 17 Sunday, May 17 Sunday, May 17 CP4 CP5 CP6 Topics in Computational Topics in Biological Topics in Bifurcation Theory Dynamical Systems I Dynamics I 4:30 PM-6:30 PM 4:30 PM-6:30 PM 4:30 PM-6:10 PM Room:Wasatch A Room:Magpie A Room:Magpie B Chair: Shibabrat Naik, Virginia Tech, Chair: Dinesh Kasti, Florida Atlantic Chair: Suma Ghosh, Pennsylvania State USA University, USA University, USA 4:30-4:45 Structuring and Stability of 4:30-4:45 Expanded Mixed Finite 4:30-4:45 A Mathematical Model for Solutions of the Static Cahn-Hilliard Element Method for Generalized the Sexual Selection of Extravagant Equation Forchheimer Flows and Costly Mating Displays Santiago Madruga, Universidad Politécnica Thinh T. Kieu, University of North Georgia, Sara Clifton, Daniel Abrams, and Daniel de Madrid, Spain; Fathi Bribesh, Zawia USA; Akif Ibraguimov, Texas Tech Thomas, Northwestern University, USA University, Libya; Uwe Thiele, University of Muenster, Germany University, USA 4:50-5:05 A Model for Mountain Pine 4:50-5:05 An Algorithmic Approach Beetle Outbreaks in An Age Structured 4:50-5:05 Sensitivity of the Dynamics to Computing Lattice Structures of Forest: Approximating Severity and of the General Rosenzweig-MacArthur Attractors Outbreak-Recovery Cycle Period Model to the Mathematical Form of the Functional Response: a Bifurcation Dinesh Kasti and William D. Kalies, Jacob P. Duncan, James Powell, and Luis Theory Approach Florida Atlantic University, USA; Robertus Gordillo, Utah State University, USA; Vandervorst, Vrije Universiteit Amsterdam, Joseph Eason, University of Utah, USA Gunog Seo, Colgate University, USA; Gail Wolkowicz, McMaster University, Canada The Netherlands 5:10-5:25 Host-Mediated Responses 5:10-5:25 Prediction in Projection on the Dynamics of Host-Parasite 5:10-5:25 Continuation of Bifurcations in Physical Experiments Joshua Garland and Elizabeth Bradley, Interaction , University of Bristol, University of Colorado Boulder, USA Suma Ghosh and Matthew Ferrari, David A. Barton Pennsylvania State University, USA United Kingdom 5:30-5:45 A Method for Identification of Spatially-Varying Parameters 5:30-5:45 Mathematical Models of 5:30-5:45 Escape from Potential Wells Despite Missing Data with Application Seasonally Migrating Populations in Multi-Degree of Freedom Systems: to Remote Sensing John G. Donohue and Petri T. Piiroinen, Phase Space Geometry and Partial Control Sean Kramer, Norwich University, USA; National University of Ireland, Galway, and Shane D. Ross, Virginia Erik Bollt, Clarkson University, USA Ireland Shibabrat Naik Tech, USA 5:50-6:05 Bifold Visualization of 5:50-6:05 Geometric Dissection of a Dynamic Networks Model for the Dynamics of Bipolar 5:50-6:05 Experimental Verification of Criteria for Escape from a Potential Yazhen Jiang, Joseph Skufca, and Jie Sun, Disorders Well in a Multi-degree of Freedom Clarkson University, USA Ilona Kosiuk, Max Planck Institute for System Mathematics in the Sciences, Germany; 6:10-6:25 Sparse Sensing Based Ekaterina Kutafina, AGH University Shane D. Ross, Virginia Tech, USA; Amir Detection of Dynamical Phenomena of Science and Technology, Poland; BozorgMagham, University of Maryland, and Flow Transitions Peter Szmolyan, Vienna University of College Park, USA; Lawrence Virgin, Duke Piyush Grover, Mitsubishi Electric Technology, Austria University, USA Research Laboratories, USA; Boris 6:10-6:25 Periodic Social Niche Kramer, Virginia Tech, USA; Petros Construction Boufounos and Mouhacine Benosman, Philip Poon, University of Wisconsin, Mitsubishi Electric Research Laboratories, Madison, USA; David Krakauer and Jessica USA Flack, Wisconsin Institute for Discovery, USA 26 2015 SIAM Conference on Applications of Dynamical Systems

Sunday, May 17 Sunday, May 17 Sunday, May 17 CP7 CP8 CP9 Topics in Mechanical Topics in Biological Non-smooth Dynamical Systems Dynamics II Systems 4:30 PM-6:10 PM 4:30 PM-6:30 PM 4:30 PM-5:50 PM Room:Wasatch B Room:Maybird Room:Superior A Chair: Thomas Ward, Iowa State Chair: Luis Mier-y-Teran, Johns Chair: John Hogan, Bristol Centre for University, USA Hopkins Bloomberg School of Public Applied Nonlinear Mathematics and 4:30-4:45 Numerical Simulations of Health, USA University of Bristol, United Kingdom Nonlinear Dynamics of Beams, Plates, 4:30-4:45 Coexistence of Multiannual 4:30-4:45 On the Use of Blow Up to and Shells Attractors in a Disease Interaction Study Regularizations of Singularities Timur Alexeev, University of California, Model: Whooping Cough Revisited of Piecewise Smooth Dynamical Davis, USA Samit Bhattacharyya, Matthew Ferrari, Systems and Ottar Bjornstad, Pennsylvania State 4:50-5:05 Global Attractors for Kristian Uldall Kristiansen, Technical University, USA Quasilinear Parabolic-Hyperbolic University of Denmark, Denmark; Equations Governing Longitudinal 4:50-5:05 Order Reduction and John Hogan, Bristol Centre for Applied Motions of Nonlinearly Viscoelastic Efficient Implementation of Nonlinear Nonlinear Mathematics and University of Rods Nonlocal Cochlear Response Models Bristol, United Kingdom Suleyman Ulusoy, Zirve University, Turkey; Maurice G. Filo, University of California, 4:50-5:05 C∞ Regularisation of Local Stuart S Antman, University of Maryland, Santa Barbara, USA Singularities of Filippov Systems USA 5:10-5:25 Periodic Outbreaks in Carles Bonet and Tere M. Seara-Alonso, 5:10-5:25 Revision on the Equation of Models of Disease Transmission with a Universitat Politecnica de Catalunya, Spain Nonlinear Vibration of the Cable with Behavioral Response 5:10-5:25 Filippov Unplugged --- Part 1 Large Sag Winfried Just, Ohio University, USA; Joan John Hogan, Bristol Centre for Applied Kun Wang, University of Macau, China Saldana, Universitat de Girona, Spain Nonlinear Mathematics and University of 5:30-5:45 Control Strategies for 5:30-5:45 Competition and Invasion Bristol, United Kingdom; Martin Homer, Electrically Driven Flapping of a of Dengue Viruses in Vaccinated Mike R. Jeffrey, and Robert Szalai, Flexible Cantilever Perturbed by Low Populations University of Bristol, United Kingdom Speed Wind Luis Mier-y-Teran and Isabel Rodriguez- 5:30-5:45 Filippov Unplugged - Part 2 Thomas Ward, Iowa State University, USA Barraquer, Johns Hopkins Bloomberg John Hogan, Bristol Centre for Applied 5:50-6:05 A New Mathematical School of Public Health, USA; Ira B. Nonlinear Mathematics and University of Explanation of What Triggered the Schwartz, Naval Research Laboratory, Bristol, United Kingdom; Martin Homer, Catastrophic Torsional Mode of the USA; Derek Cummings, Johns Hopkins Mike R. Jeffrey, and Robert Szalai, Tacoma Narrows Bridge Bloomberg School of Public Health, USA University of Bristol, United Kingdom Gianni Arioli, Politecnico di Milano, Italy 5:50-6:05 Examining Ebola Transmission Dynamics and Forecasting Using Identifiability and Parameter Estimation Marisa Eisenberg, University of Michigan, USA 6:10-6:25 How Radiation-Induced Dedifferentation Influences Tumor Hierarchy Kimberly Fessel, Mathematical Biosciences Institute, USA; John Lowengrub, University of California, Irvine, USA 2015 SIAM Conference on Applications of Dynamical Systems 27

Sunday, May 17 Sunday, May 17 Sunday, May 17 CP10 CP11 CP12 Topics in Geometric and Topics in Feedback/Control/ Topics in Atmospheric/ Nonlinear Dynamical Optimization I Climate Dynamics and Systems 4:30 PM-6:30 PM Related Themes 4:30 PM-6:30 PM Room:White Pine 4:30 PM-6:10 PM Room:Superior B Chair: Kathrin Flaßkamp, Northwestern Room:Primrose A Chair: Colin J. Grudzien, University of University, USA Chair: Miklos Vincze, Hungarian North Carolina at Chapel Hill, USA 4:30-4:45 Computing Bisimulation Academy of Sciences, Hungary 4:30-4:45 Tensor of Green of Coupled Functions Using SoS Optimization and 4:30-4:45 Gradual and Abrupt Regime Thermoelastodynamics δ-Decidability over the Reals Shifts in Drylands Bakhyt Alipova, University of Kentucky, Abhishek Murthy, Philips Research North Yuval Zelnik, Ehud Meron, and Golan Bel, USA America, USA; Md. Ariful Islam and Ben-Gurion University of the Negev, Israel Scott Smolka, Stony Brook University, 4:50-5:05 Baroclinic Instability in An 4:50-5:05 Geometric Phase in the USA; Radu Grosu, Vienna University of Initially Stratified Rotating Fluid Hopf Bundle and the Sability of Non- Technology, Austria Linear Waves Miklos P. Vincze, Hungarian Academy of Colin J. Grudzien and Christopher Krt 4:50-5:05 Chaos in Biological Systems Sciences, Hungary; Patrice Le Gal, CNRS Jones, University of North Carolina at with Memory and Its Controllability & Aix-Marseille Université, Marseille, Chapel Hill, USA Mark Edelman, Stern College for Women France; Uwe Harlander, Brandenburg and Courant Institute of Mathematical University of Technology, Germany 5:10-5:25 Error Assessment of the Sciences, New York University, USA Local Statistical Linearization Method 5:10-5:25 Modified Lorenz Equations Leo Dostal and Edwin Kreuzer, Hamburg 5:10-5:25 Odd-Number Limitation for for Rotating Convection University of Technology, Germany Extended Time-Delayed Feedback Jessica Layton, Jared P. Whitehead, Control and Shane McQuarrie, Brigham Young 5:30-5:45 Curve Evolution in Second- Andreas Amann and Edward Hooton, University, USA Order Lagrangian Systems University College Cork, Ireland Ronald Adams and William D. Kalies, 5:30-5:45 Empirical Validation of Florida Atlantic University, USA; 5:30-5:45 Approximate Controllability Conceptual Climate Models R.C.A.M van Der Vorst, Vrije Universiteit of An Impulsive Neutral Fractional Charles D. Camp, Ryan Smith, and Andrew Stochastic Differential Equation With Amsterdam, The Netherlands Gallatin, California Polytechnic State Deviated Argument and Infinite Delay University, USA 5:50-6:05 Periodic Sanjukta Das and Dwijendra Pandey, Indian Eigendecomposition and Its Institute of Technology Roorkee, India 5:50-6:05 On the Geometry of Application in Nonlinear Dynamics Attractors in Ageostrophic Flows with Xiong Ding and Predrag Cvitanovic, 5:50-6:05 Mathematical Study of the Viscoelastic-Type Reynolds Stress Effects of Travel Costs on Optimal Georgia Institute of Technology, USA Maleafisha Stephen Tladi, University of Dispersal in a Two-Patch Model Limpopo, South Africa 6:10-6:25 Computation of Cauchy- Theodore E. Galanthay, Ithaca College, Green Strain Tensor Using Local USA Regression Shane D. Kepley and Bill Kalies, Florida 6:10-6:25 Discrete-Time Structure- Preserving Optimal Ergodic Control Atlantic University, USA Kathrin Flaßkamp and Todd Murphey, Northwestern University, USA 28 2015 SIAM Conference on Applications of Dynamical Systems

Sunday, May 17 Sunday, May 17 Monday, May 18 CP13 Prize Presentations - Jürgen Moser and Topics in Nonlinear J. D. Crawford Registration Oscillators 8:00 PM-8:15 PM 8:00 AM-6:30 PM 4:30 PM-6:10 PM Room:Ballroom Room:Ballroom Foyer Room:Primrose B J. D. Crawford Prize Recipient: Chair: Punit R. Gandhi, University of Florin Diacu, University of Victoria, Canada California, Berkeley, USA MS5 4:30-4:45 Localized States in Periodically Forced Systems Structural and Functional Punit R. Gandhi, University of California, SP1 Network Dynamics and Berkeley, USA; Cedric Beaume, Imperial Inference College London, United Kingdom; Edgar Jürgen Moser Lecture - Knobloch, University of California, Dynamics and Data 8:30 AM-10:30 AM Berkeley, USA 8:15 PM-9:00 PM Room:Magpie B 4:50-5:05 Multicluster and Traveling Room:Ballroom Complex systems are ubiquitous in nature, Chimera States in Nonlocal Phase- yet there often remains a disconnect Coupled Oscillators Chair: Timothy Sauer, George Mason between models and real-world systems. Hsien-Ching Kao, Wolfram Research Inc., University, USA This discrepancy can be manifest as limited USA; Jianbo Xie and Edgar Knobloch, This lecture highlights interdisciplinary knowledge about the ordinary and/or University of California, Berkeley, USA interactions of dynamical systems theory. partial differential equations, the network 5:10-5:25 Chimera States on the Route Experimental data and computer simulation encoding which variables interact, or both. from Coherent State to a Rotating have inspired mathematical discoveries, System identification such as the inference Wave while resulting theory has made successful of “structural” and “functional networks” is Tomasz Kapitaniak, Technical University of predictions and created new scientific thus an unavoidable hurdle for the realistic Lodz, Poland perspectives. Nonlinear dynamics has unified modeling of many complex systems. We will diverse fields of science and revealed deep study structural and functional networks arising 5:30-5:45 Onset and Characterization mathematical phenomena. in biological and physical systems as well of Chimera States in Coupled as explore various network analyses such as Examples involving Nonlinear Oscillators community detection and motif extraction. Lakshmanan Muthusamy, Bharathidasan • One dimensional maps University, India Organizer: Dane Taylor • Numerical bifurcation analysis University of North Carolina at Chapel 5:50-6:05 Emergent Rhythmic Behavior • Multiple time scales Hill, USA of Mixed-Mode Oscillations in Pulse- • Bursting and MMOs in neuroscience and 8:30-8:55 Causal Network Inference by Coupled Neurons chemistry Optimal Causation Entropy Avinash J. Karamchandani, James • Locomotion Graham, and Hermann Riecke, Jie Sun and Erik Bollt, Clarkson University, Northwestern University, USA are described, along with emerging areas USA; Dane Taylor, University of North having public impact. Carolina at Chapel Hill, USA John Guckenheimer, Cornell University, 9:00-9:25 A Complex Networks USA Approach to Malaria’s Genetic Dinner Break Recombination Dynamics 6:30 PM-8:00 PM Daniel B. Larremore and Caroline Buckee, Harvard School of Public Health, USA; Attendees on their own Aaron Clauset, University of Colorado Boulder, USA 9:30-9:55 Combined Effects of DSWeb Editorial Board Meeting Connectivity and Inhibition in a Model 6:30 PM-8:00 PM of Breathing Rhythmogenesis Kameron D. Harris, University of Room: Boardroom Washington, USA; Tatiana Dashevskiy, Seattle Children’s Research Institute, USA; Eric Shea-Brown and Jan-Marino Ramirez, University of Washington, USA 10:00-10:25 Not-So-Random Graphs Through Wide Motifs Pierre-Andre Noel, University of California, Davis, USA 2015 SIAM Conference on Applications of Dynamical Systems 29

Monday, May 18 Monday, May 18 9:30-9:55 Symmetry Breaking and Synchronization Patterns in Networks MS19 MS20 of Coupled Oscillators Francesco Sorrentino, University of New Patterns in Partial Differential Structure-dynamics Relation Mexico, USA; Aaron M. Hagerstrom, Equations - Part II of II in Networks of Coupled University of Maryland, USA; Louis M. Dynamical Systems Pecora, Naval Research Laboratory, USA; 8:30 AM-10:30 AM Thomas E. Murphy and Rajarshi Roy, Room:Ballroom I 8:30 AM-10:30 AM University of Maryland, College Park, USA For Part 1 see MS1 Room:Ballroom II Patterns play an important role in the A fundamental question in studying 10:00-10:25 Homeostasis As a dynamics of many dissipative and dispersive coupled dynamical systems concerns the Network Invariant PDEs, posed on large or unbounded dynamics-structure relation -- how do the Martin Golubitsky, The Ohio State domains. This minisymposium will feature characteristics of the interactions between University, USA; Ian Stewart, University contributions that investigate intrinsically dynamical units determine the dynamical of Warwick, United Kingdom multi-dimensional aspects of the dynamics behavior of the system? After more than a of patterns, including their existence, decade of research on the structure of real stability, instability, slow evolution, and networks, the problem of understanding this interaction. Examples include interfaces relation has become a major topic of interest between patterned and un-patterned state, in the dynamical systems community. This point defects or vortices, and line defects. minisymposium will address this timely We expect to bring together researchers topic, focusing on network-dynamical with a variety of backgrounds, employing phenomena, such as synchronization patterns, a variety of techniques, such as diffusive sensitive dependence of dynamical stability, and dispersive stability estimates, energy and homeostasis, and using a range of methods from the calculus of variations, or mathematical tools from graph theory, linear spatial dynamics and bifurcation methods. algebra, group theory, and optimization. Organizer: Keith Promislow Organizer: Francesco Sorrentino Michigan State University, USA University of New Mexico, USA Organizer: Noa Kraitzman Organizer: Takashi Nishikawa Michigan State University, USA Northwestern University, USA 8:30-8:55 Existence of Pearled 8:30-8:55 Optimized Networks Have Patterns in the Planar Functionalized Cusp-like Dependence on Structural Cahn-Hilliard Equation Parameters Qiliang Wu, Michigan State University, Takashi Nishikawa and Adilson E. Motter, USA Northwestern University, USA 9:00-9:25 Stability in Spatially 9:00-9:25 Symmetries, Cluster Localized Patterns Synchronization, and Isolated Elizabeth J. Makrides and Bjorn Desynchronization in Complex Sandstede, Brown University, USA Networks 9:30-9:55 Reformulating Spectral Louis M. Pecora, Naval Research Problems with the Krein Matrix Laboratory, USA; Francesco Sorrentino, Todd Kapitula, Calvin College, USA University of New Mexico, USA; Aaron M. Hagerstrom, University of Maryland, 10:00-10:25 A Geometric Approach USA; Rajarshi Roy and Thomas E. to Stationary Defect Solutions Murphy, University of Maryland, College Arjen Doelman, Leiden University, Park, USA Netherlands; Peter van Heijster, Queensland University of Technology, Australia; Feng Xie, Leiden University, Netherlands

continued in next column 30 2015 SIAM Conference on Applications of Dynamical Systems

Monday, May 18 Monday, May 18 Monday, May 18 MS21 MS22 MS24 Ocean-in-the-loop: Towards Geometric Mechanics and Nontwist Hamiltonian Real-Time Monitoring in Applications systems: Theory and Geophysical Flows - 8:30 AM-10:30 AM Applications Part II of II Room:Magpie A 8:30 AM-10:30 AM 8:30 AM-10:30 AM This minisymposium will focus on Room:Wasatch A the application of geometric methods Room:Ballroom III In recent years, more and more physical to dynamical systems originating in systems have been found that can be modeled For Part 1 see MS3 mechanicals. The geometric viewpoint by Hamiltonians that locally violate a non- Improved modeling and prediction of fluid provides a unified and systematic framework degeneracy condition leading to the appearance dynamics is needed to better understand to address a broad range of problems, of so-called shearless invariant tori which ocean and atmospheric transport along with including control, numerical integration, and act as particularly robust transport barriers associated applications including contaminant qualitative dynamics, for both finite- and in phase space. This minisymposium brings dispersion, environmental modeling, and infinite-dimensional systems. In particular, together researchers from physics and applied underwater acoustic propagation. Major recent topics represented include the geometric mathematics to present the latest developments advances in closed-loop adaptive sampling, optimal control of mechanical systems, and applications in the subject of nontwist Lagrangian data assimilation, uncertainty stability analysis, variational principles, the Hamiltonian systems. Recent numerical studies quantification, and phase space transport use of momentum maps, and variational of breakup and emergence of shearless tori are providing improved understanding of integrators. This minisymposium provides and applications in plasma physics will be transport phenomena. The purpose of this a unique opportunity for mathematicians, discussed. minisymposium is to expose the audience to applied mathematicians, and engineers to recent progress and developments, as well as come together and explore their common Organizer: Alexander Wurm to bring together researchers developing new interest in the geometric approach to Western New England University, USA mathematical methods and applications for use mechanics. Organizer: P. J. Morrison in understanding flow transport. Organizer: Vakhtang Putkaradze University of Texas at Austin, USA Organizer: Eric Forgoston University of Alberta, Canada 8:30-8:55 Breakup of Shearless Tori and Montclair State University, USA 8:30-8:55 The Geometry of the Toda Reconnection in the Piecewise-Linear Organizer: Ani Hsieh Lattice Map Standard Nontwist Map Drexel University, USA Anthony M. Bloch, University of Michigan, Alexander Wurm, Western New England USA University, USA 8:30-8:55 Optimal Control in Lagrangian Data Assimilation 9:00-9:25 Dynamics and Optimal 9:00-9:25 Nontwist Worm Map Damon Mcdougall, University of Texas Control of Flexible Solar Updraft Caroline G. L. Martins and P. J. Morrison, at Austin, USA; Richard O. Moore, New Towers University of Texas at Austin, USA; J. D. Jersey Institute of Technology, USA Vakhtang Putkaradze, University of Szezech, Universidade Estadual de Ponta Alberta, Canada Grossa, Brazil; I. L. Caldas, Universidade de 9:00-9:25 A Hybrid Particle-Ensemble Sao Paulo, Brazil Kalman Filter for High Dimensional 9:30-9:55 Geodesic Finite Elements Lagrangian Data Assimilation on Symmetric Spaces and Their 9:30-9:55 Breakup of Tori in Elaine Spiller, Marquette University, USA; Applications to Multisymplectic Multiharmonic Nontwist Standard Maps Laura Slivinski, Woods Hole Oceanographic Variational Integrators Adam M. Fox, Western New England Institute, USA; Amit Apte, TIFR Centre, Phillip Grohs, ETH Zürich, Switzerland; University, USA; James D. Meiss, University Bangalore, India Melvin Leok, Joe Salamon, and John of Colorado Boulder, USA 9:30-9:55 A Multi Agent Control Moody, University of California, San 10:00-10:25 Influence of Finite Larmor Strategy for Sampling Uncertain Diego, USA Radius on Critical Parameters for Spatio-Temporally Varying Flow Fields 10:00-10:25 Hamel’s Formalism for Invariant Curves Break Up in Area Axel Hackbarth and Edwin Kreuzer, Infinite-Dimensional Mechanical Preserving Maps Models of ExB Chaotic Hamburg University of Technology, Systems Transport Germany Dmitry Zenkov, North Carolina State Julio Fonseca, University of Sao Paulo, University, USA Brazil; Diego Del-Castillo-Negrete, Oak 10:00-10:25 Bayesian Nonlinear Ridge National Laboratory, USA; Iberê L. Assimilation for Eulerian Fields and Caldas, Universidade de Sao Paulo, Brazil Lagrangian Trajectories Pierre Lermusiaux, Massachusetts Institute of Technology, USA 2015 SIAM Conference on Applications of Dynamical Systems 31

Monday, May 18 Monday, May 18 Monday, May 18 MS25 MS26 MS27 Rhythmic Dynamics of Experiments on Transport in Analysis of Network Minimal Neuronal Networks Multi-scale Fluid Systems Dynamical Systems 8:30 AM-10:30 AM 8:30 AM-10:30 AM 8:30 AM-10:30 AM Room:Wasatch B Room:Maybird Room:Superior A Recent trends in mathematical and Transport in fluid systems is mainly Many real world dynamical systems admit computational neuroscience have led to investigated by theoretical and numerical a nontrivial network structure. This special studies of increasingly larger networks. methods. Experimental studies lag behind structure often makes these systems behave However, there are still many fundamental yet are crucial both for validation purposes in an unexpected way. Networks can for questions related to the dynamics of rhythmic and for investigation of phenomena that are example synchronise, support anomalous networks that are best suited to be addressed beyond theory and simulations. The aims of bifurcations, admit robust heteroclinic in the context of small and minimal models. these investigations range from validation cycles, display chimera states, etc. In Speakers in this minisymposium will focus of fundamental transport phenomena to other words: dynamical behaviour that is on questions that involve multiple time bridging the gap from dynamical-systems classically considered “degenerate” and scales, the detection of synchrony and the concepts to (industrial) applications. This hence “irrelevant”, turns out to be generic coordination of neural activity in the context mini-symposium highlights the essential role in the context of networks, and can thus of central pattern generators and more of laboratory experiments in comprehensive be important for applications. In this general brain networks. A primary goal is transport studies of multi-scale systems, minisymposium, we present a number of to use mathematical modeling to identify which are almost the only class of flows that recent insights in the analysis of networks biological mechanisms that underlie the allows analytical description and presents that may be used to understand and predict existence and control of rhythms. Because of a natural meeting point for experiments, their dynamical behaviour. the minimal nature of the models considered, simulations and theory. Organizer: Bob Rink mathematical findings can fairly clearly be Organizer: Michel Speetjens VU University, Amsterdam, Netherlands correlated to biological mechanisms. Eindhoven University of Technology, Organizer: Eddie Nijholt Organizer: Amitabha Bose Netherlands VU University, Amsterdam, Netherlands New Jersey Institute of Technology, USA Organizer: Dmitri Vainchtein 8:30-8:55 Classifying Bifurcations in 8:30-8:55 The Role of Voltage- Temple University, USA Coupled Cell Networks Dependent Electrical Coupling in the Control of Oscillations 8:30-8:55 Chaotic Mixing and Eddie Nijholt, Bob Rink, and Jan Sanders, Christina Mouser, William Patterson Transport Barriers VU University, Amsterdam, Netherlands University, USA; Farzan Nadim and Thomas H. Solomon, Bucknell University, 9:00-9:25 Pulse Bifurcations in Amitabha Bose, New Jersey Institute of USA Stochastic Neural Fields Technology, USA 9:00-9:25 How Small a Thought: Design Zachary Kilpatrick, University of Houston, USA; Gregory Faye, École des Hautes 9:00-9:25 Understanding and of Mixing and Separation Processes Distinguishing Multiple Time Scale with Dynamical Systems Etudes en Sciences Sociales, France Oscillations Guy Metcalfe, CSIRO, Australia 9:30-9:55 Dynamics of Asynchronous Yangyang Wang and Jonathan E. Rubin, 9:30-9:55 3D Chaotic Advection in Networks University of Pittsburgh, USA Langmuir Cells Christian Bick, Rice University, USA; 9:30-9:55 The Essential Role of Phase Larry Pratt and Irina Rypina, Woods Hole Michael Field, Imperial College London, Delayed Inhibition in Decoding Oceanographic Institute, USA United Kingdom; Anushaya Mohapatra, Oregon State University, USA Synchronized Oscillations 10:00-10:25 Experimental Investigation Badal Joshi, California State University, San of Fundamental Lagrangian Transport 10:00-10:25 Dynamics of Marcos, USA; Mainak Patel, College of Phenomena Heterogeneous Networks: Reductions William & Mary, USA Michel Speetjens, Eindhoven University of and Coherent Behaviour 10:00-10:25 Neural Mechanisms of Technology, Netherlands Tiago Pereira, Universidade de Sao Paulo, Limb Coordination in Crustacean Brazil; Matteo Tanzi and Sebastian van Swimming Strien, Imperial College London, United Kingdom Tim Lewis, University of California, Davis, USA 32 2015 SIAM Conference on Applications of Dynamical Systems

Monday, May 18 Monday, May 18 Monday, May 18 MS28 MS29 MS30 Simple Systems with Multiscale Models to Network Synchronization in Complex Dynamics Understand the Social and Mechanical Systems and 8:30 AM-10:30 AM Physical World - Part II of II Beyond - Part II of II Room:Superior B 8:30 AM-10:30 AM 8:30 AM-10:30 AM Lab experiments can often be very costly Room:White Pine Room:Primrose A as they may require expensive equipment. For Part 1 see MS11 For Part 1 see MS12 However, research in dynamical systems The scientific community has developed This minisymposium focuses on the role can still be done using simple table top a rich and diverse library of mathematical of synchronization, coordination, and experiments at low cost. Many of these models capable of capturing complex dynamical consensus in mechanical systems systems may seem extremely simple processes and interactions over a broad range and beyond. Examples range from bridges and mundane in set up, yet they can of scales in space and time. In this session, and mechanical pendula to self-organizing be very rich in their dynamics. In this we feature a variety of researchers exploring networks of moving agents, with application mini-symposium, we present four table the application of mathematical models to the in robotics and animal behavior. This top experiments involving mechanical, social and physical world. The topics of this minisymposium aims at various theoretical chemical and electrical oscillators and session cover several scales, from interacting and experimental aspects of synchrony- show how they can produce complex particles to population models to PDEs, and induced phenomena and their control and phenomena such as synchronization, include both stochastic and deterministic brings together applied mathematicians and period doubling bifurcation and chaos. We models. Talks will address applications such mechanical engineers. also demonstrate how these systems can be as earthquakes, swimming microorganisms, Organizer: Igor Belykh studied mathematically and numerically. and human crowd dynamics. Georgia State University, USA Organizer: Andrea J. Welsh Organizer: Alethea Barbaro Organizer: Maurizio Porfiri Georgia Institute of Technology, USA Case Western Reserve University, USA Polytechnic Institute of New York 8:30-8:55 Period Doubling in the Organizer: Brittany Erickson Saline Oscillator University, USA Portland State University, USA Diandian Diana Chen and Flavio 8:30-8:55 Synchronization in Fenton, Georgia Institute of Technology, 8:30-8:55 Population Models Applied Dynamical Networks of Noisy USA to Model the Pregnancy to Labor Nonlinear Oscillators, Or Collective Transition Behavior of Zebrafish 9:00-9:25 Oscillatory Dynamics of Douglas Brubaker, Alethea Barbaro, Mark Violet Mwaffo and Ross Anderson, New the Candelator Chance, and Sam Mesiano, Case Western York University Polytechnic, USA; Greg A. Byrne, Mary Elizabeth Lee, Reserve University, USA Maurizio Porfiri, Polytechnic Institute of and Flavio Fenton, Georgia Institute of New York University, USA Technology, USA 9:00-9:25 Stochastic Fluctuations in Suspensions of Swimming 9:00-9:25 Synchronization of a 9:30-9:55 Synchronization Microorganisms Nonlinear Beam Coupled with Patterns in Simple Networks of Peter R. Kramer, Yuzhou Qian, and Patrick Deformable Substrates Optoelectronic Oscillators Underhill, Rensselaer Polytechnic Institute, Briana Mork, Gustavus Adolphus College, Davide Spinello, University of Ottawa, USA USA; Kate Coppess, University of Canada Michigan, Ann Arbor, USA; Caitlin 9:30-9:55 A Model for Riot Dynamics: 9:30-9:55 A Self-Organising R. S. Williams, Washington and Lee Shocks, Diffusion and Thresholds Distributed Strategy for Optimal University, USA; Aaron M. Hagerstrom Nancy Rodriguez-Bunn, University of Synchronisation of Networked and Joseph Hart, University of North Carolina at Chapel Hill, USA; Henri Mechanical Systems Maryland, USA; Thomas E. Murphy, Berestycki and Jean-Pierre Nadal, CNRS, Louis Kempton, Guido Hermann, and University of Maryland, College Park, France Mario Di Bernardo, University of Bristol, USA; Rajarshi Roy, University of 10:00-10:25 Crowd Modeling: How United Kingdom Maryland, USA Can People Respond to Fear 10:00-10:25 Synchronization Control 10:00-10:25 Noise-Induced Jesus Rosado Linares, Universidad of Electrochemical Oscillator Transitions in Bistable Tunnel Diode de Buenos Aires, Argentina; Alethea Assemblies by External Inputs Circuits Barbaro, Case Western Reserve University, Anatoly Zlotnik, Los Alamos National Stephen Teitsworth, Yuriy Bomze, USA; Andrea L. Bertozzi, University of Laboratory, USA; Istvan Z. Kiss and Steven Jones, and Ryan McGeehan, California, Los Angeles, USA Raphael Nagao, Saint Louis University, Duke University, USA USA; Jr-Shin Li, Washington University, St. Louis, USA 2015 SIAM Conference on Applications of Dynamical Systems 33

Monday, May 18 Monday, May 18 Monday, May 18 MS31 IP2 MS32 Extreme Events: Modeling, Mathematics of Crime Energy Transfer and Analysis, Prediction, and 11:00 AM-11:45 AM Harvesting in Nonlinear Control Systems - Part I of II Room:Ballroom 8:30 AM-10:30 AM Chair: Michelle Girvan, University of 1:15 PM-3:15 PM Room:Primrose B Maryland, USA Room:Ballroom I Extreme events are considered to be rare There is an extensive applied mathematics For Part 2 see MS45 events characterized by a large impact on a literature developed for problems in the The minisymposium will focus on recent particular system which is measured in terms biological and physical sciences. Our developments and challenges related to of some observable or order parameter. The understanding of social science problems energy transfer and harvesting in nonlinear aim of this minisymposium is to discuss the from a mathematical standpoint is less systems. Special attention will be paid mechanisms of generation of extreme events as developed, but also presents some very to rapidly developing research field of well as their prediction and control in different interesting problems, especially for young nonsmooth systems. Topics will include, but system classes which are relevant to different researchers. This lecture uses crime as a will not be limited to: applications in nature. The system classes case study for using applied mathematical • New results in the classical problem of covered by this minisymposium are excitable techniques in a social science application and divergent vs convergent heat conduction population dynamical systems, coupled covers a variety of mathematical methods in models of atomic lattices; systems, stochastic multistable systems as well that are applicable to such problems. We • Description of wave initiation, as small-world networks of excitable units of will review recent work on agent based propagation and mitigation in granular FitzHugh Nagumo type. models, methods in linear and nonlinear systems; partial differential equations, variational Organizer: Ulrike Feudel • Nonlinear targeted energy transfer University of Oldenburg, Germany methods for inverse problems and statistical point process models. From an application in systems with strongly nonlinear Organizer: Klaus Lehnertz standpoint we will look at problems in attachments University of Bonn, Germany residential burglaries and gang crimes. • Applications of strong and non-smooth nonlinearities for efficient energy 8:30-8:55 Extreme Events in Nature: Examples will consider both “bottom up’ harvesting. Harmful Algal Blooms and ‘top down’ approaches to understanding Ulrike Feudel, University of Oldenburg, the mathematics of crime, and how the two Organizer: Oleg Gendelman Germany; Subhendu Chakraborty, DTU approaches could converge to a unifying Technion Israel Institute of Technology, theory. Aqua, Denmark; Cornelius Steinbrink, Rajat Israel Karnatak, and Helmut Hillebrand, University Andrea L. Bertozzi Organizer: Alexander Vakakis of Oldenburg, Germany University of California, Los Angeles, University of Illinois, USA 9:00-9:25 Extreme Events on Small- USA World Networks of Excitable Units 1:15-1:40 Convergent Heat Conduction in One-Dimensional Gerrit Ansmann and Klaus Lehnertz, Lattices with Dissociation University of Bonn, Germany; Ulrike Feudel, , Technion Israel Institute University of Oldenburg, Germany Lunch Break Oleg Gendelman of Technology, Israel; Alexander Savin, 9:30-9:55 Extreme Events in Stochastic 11:45 AM-1:15 PM Institute of Chemical Physics, Moscow, Multistable Systems Attendees on their own Russia Alexander N. Pisarchik, Technical University 1:45-2:10 Stochastic Closure Schemes of Madrid, Spain; Ricardo Sevilla-Escoboza, for Bi-stable Energy Harvesters Guillermo Huerta-Cuellar, and Rider Jaimes- Excited by Colored Noise Reátegui, Universidad de Guadalajara, Mexico Themistoklis Sapsis and Han Kyul Joo, 10:00-10:25 Forecasting and Controlling Massachusetts Institute of Technology, Dragon-King Events in Coupled USA Dynamical Systems 2:15-2:40 Bistable Nonlinear Energy Daniel J. Gauthier, Duke University, Sink Coupled System for Energy USA; Hugo Cavalcante and Marcos Oria, Absorption and Harvesting Universidade Federal da Paraiba, Brazil; Francesco Romeo, University of Rome Didier Sornette, ETH Zürich, Switzerland; La Sapienza, Italy; Giuseppe Habib, Ed Ott, University of Maryland, USA University of Liege, Belgium 2:45-3:10 Acceleration of Charged Coffee Break Particles in the Presence of 10:30 AM-11:00 AM Fluctuations Africa Ruiz Mora and Dmitri Vainchtein, Room:Golden Cliff Temple University, USA 34 2015 SIAM Conference on Applications of Dynamical Systems

Monday, May 18 Monday, May 18 Monday, May 18 MS33 MS34 MS35 Rare Events in Stochastic Mathematical Models of Dynamics of Inertial Particles Systems Cancer Development and in Flows 1:15 PM-3:15 PM Treatment 1:15 PM-3:15 PM Room:Ballroom II 1:15 PM-3:15 PM Room:Magpie A A pivotal goal in the analysis of dynamical Room:Ballroom III The dynamics of particles in fluid flows is of systems is the prediction and qualitative Cancer develops in stages from incipience to fundamental importance in a wide range of description of long-term behavior. In metastasis, often followed by the emergence scientific problems. Heavy particles respond deterministic systems, this is often of drug resistance and evasion of the immune in intricate ways to fluid-velocity fluctuations. accomplished via bifurcation analysis and response. Understanding cancer progression Recently there has been substantial progress in the identification of invariant motions, and interaction with treatments will lead to understanding the dynamics of such particles usually considering the behavior of orbits. insights into cancer therapy by aiding the by analysing simplified mathematical models. Most practical systems however are noisy, design of innovative strategies that include Most models neglect the effect of fluid inertia and even in the presence of small noise and combine chemotherapy, virotherapy, although it can have a substantial effect in a stochastic system will exhibit events immunotherapy, and other approaches. certain cases. The goal of this minisymposium that cannot be described by deterministic Current mathematical models seek to is to discuss recent developments in dynamics alone. The rarity of such events understand cancer deterministically and understanding the role of fluid inertia upon the necessitates specialized tools and approaches stochastically from the level of populations motion of particles suspended in steady and in to study them. This minisymposium will to individual cells. This minisymposium will turbulent flows. focus on recent advancements in the bring together speakers who are applying a Organizer: Bernhard Mehlig methods to investigate rare events as well as variety of mathematical and computational University of Gothenburg, Sweden intriguing applications of these methods. approaches to consider various stages of 1:15-1:40 The Effect of Particle and Fluid cancer development and treatment. Organizer: Christoffer R. Heckman Inertia on the Dynamics of Particles in University of Colorado Boulder, USA Organizer: Joanna Wares Flows Organizer: Ira B. Schwartz University of Richmond, USA Bernhard Mehlig, University of Gothenburg, Naval Research Laboratory, USA Organizer: Peter S. Kim Sweden 1:15-1:40 Rare Events in Stochastic University of Sydney, Australia 1:45-2:10 Effect of Fluid and Particle Dynamical Systems with Delay: From 1:15-1:40 How Much and How Often? Inertia on the Dynamics and Scaling of Random Switching to Extinctions Mathematical Models of Cancer Ellipsoidal Particles in Shear Flow Ira B. Schwartz, Naval Research Vaccine Delivery Tomas Rosen, KTH Royal Institute of Technology, Sweden; Yusuke Kotsubo, Laboratory, USA; Thomas W. Carr, Ami Radunskaya, Pomona College, USA Southern Methodist University, USA; Tokyo University, Japan; Cyrus Aidun, Lora Billings, Montclair State University, 1:45-2:10 A Mathematical Model Georgia Institute of Technology, USA; USA; Mark Dykman, Michigan State of Cancer Stem Cell Lineage Fredrik Lundell, KTH Stockholm, Sweden Population Dynamics with Mutation University, USA Accumulation and Telomere Length 2:15-2:40 Inertia Effects in the Dynamics 1:45-2:10 Rare Event Extinction on Hierarchies of Spherical and Non-Spherical Stochastic Networks Georgi Kapitanov, University of Iowa, Objects at Low Reynolds Number Leah Shaw, College of William & Mary, USA Fabien Candelier, Aix-Marseille Université, USA; Brandon S. Lindley and Ira B. France 2:15-2:40 A Cell Population Model Schwartz, Naval Research Laboratory, Structured by Cell Age Incorporating 2:45-3:10 Influence of the History USA Cell-cell Adhesion Force on Inertial Particle Advection: 2:15-2:40 Influence of Periodic Glenn Webb, Vanderbilt University, USA Gravitational Effects and Horizontal Modulation in Extreme Optical Pulses Diffusion 2:45-3:10 Mathematical Models of the Cristina Masoller, Universitat Politecnica Ksenia Guseva and Ulrike Feudel, University Treatment of Chronic Lymphocytic de Catalunya, Spain of Oldenburg, Germany; Tamas Tel, Eötvös Leukemia with Ibrutinib and the Loránd University, Hungary 2:45-3:10 Models of Large Deviations Development of Drug Resistance and Rare Events for Optical Pulses Dominik Wodarz, University of California, William Kath, Northwestern University, Irvine, USA USA 2015 SIAM Conference on Applications of Dynamical Systems 35

Monday, May 18 Monday, May 18 Monday, May 18 MS36 MS37 MS38 Theory and Applications of Guided Approaches to Spatial Organization of Nonsmooth Dynamics in Ocean Data Assimilation Biochemical Dynamics Physical Systems - Part I of II Incorporating Uncertainty Within and Between Cells 1:15 PM-3:15 PM and Observability 1:15 PM-3:15 PM Room:Magpie B 1:15 PM-3:15 PM Room:Wasatch B For Part 2 see MS49 Room:Wasatch A Recent advances in imaging of biochemical This minisymposium will provide a mix of Ocean dynamics strongly drive transport processes has revealed spatial organization talks featuring theoretical developments in and ecological balances at all spatiotemporal of the underlying processes, which were nonsmooth systems as well as talks featuring scales, influencing seasonal and operational previously assumed homogenous or well- applications with nonsmooth dynamics. In forecasts for commerce and defense. mixed. We explore modeling methods either case, physical applications provide Prediction of ocean dynamics is challenging to describe the spatial organization of the motivation for mathematical exploration. due to sparsity and inhomogeneity of these processes within and between cells. Additionally, the minisymposium will blend observations, as well as nonlinearity of Approaches include PDE and ODE based talks appropriate for a broad audiences and dynamics and model errors contributing to models, matched asymptotic expansions, talks geared at experts. To that point, the uncertainty. These challenges may be met dominant balance analysis, and agent based minisymposium will begin with the very through data assimilation techniques that modeling. The symposium includes a range general “How nonsmooth are the Earth properly incorporate uncertainty, along with of applications: improved efficiency of sciences?” which will set the stage for the the use of distributed sampling platforms metabolic reactions through cellular spatial rest of the speakers. Other talks will discuss for in situ sampling. This session focuses on organization, quorum sensing in biofilms, issues such as generalized bifurcations, guided data assimilation for incorporating cell-fate decisions due to signaling gradients, canard phenomena, synchronization, and the uncertainty into observing system design. and the effect of the micro environment on new area of resilience. To improve overall forecast skill, we drug resistance in cancer cells. Organizer: Andrew Roberts address questions related to observability, Organizer: Niall M. Mangan Cornell University, USA identification of coherent flow structures, and Massachusetts Institute of Technology, desirable sampling trajectories. Organizer: Esther Widiasih USA University of Hawaii, West Oahu, USA Organizer: Derek A. Paley 1:15-1:40 Organization of Metabolic University of Maryland, USA Reactions for Improved Efficiency: 1:15-1:40 How Nonsmooth Are the Carbon Fixation and Bioengineering Earth Sciences? 1:15-1:40 A Quantitative Measure of Applications Chris Budd and Tim J. Dodwell, University Observability for Data Assimilations Niall M. Mangan, Massachusetts Institute of Bath, United Kingdom Wei Kang, Naval Postgraduate School, USA; Sarah King and Liang Xu, Naval of Technology, USA 1:45-2:10 The Search for Glacial Research Laboratory, USA 1:45-2:10 A 3D Model of Cell Signal Cycles: A Quasiperiodically Forced Transduction Nonsmooth System in a Conceptual 1:45-2:10 Probabilistic Approach to Climate Model Deployment Strategy in Lagrangian David Iron, Dalhousie University, Canada Esther Widiasih, University of Hawaii, Data Assimilation 2:15-2:40 Synthetic Genetic Circuits for West Oahu, USA; James Walsh, Oberlin Kayo Ide, University of Maryland, College Spatial Patterning College, USA; Richard McGehee and Park, USA Paul Steiner, University of California, San Jonathan Hahn, University of Minnesota, 2:15-2:40 Multivehicle Motion Diego, USA USA Planning in the Presence of Ocean 2:45-3:10 An Spatial Model of Anti- 2:15-2:40 Analysis of an Arctic Sea Eddies Cancer Drug Resistance: the Role of Ice Model in a Nonsmooth Limit Frank D. Lagor and Derek A. Paley, the Micro-Environment Kaitlin Hill and Mary Silber, Northwestern University of Maryland, USA Kerri-Ann Norton, Johns Hopkins University, USA 2:45-3:10 Bayesian Nonlinear University, USA; Kasia Rejniak, H. Lee 2:45-3:10 Mathematical Smoothing and Mutual Information Moffitt Cancer Center & Research Institute, Quantifications of Resilience for Adaptive Sampling USA; Jana Gevertz, The College of New Jersey, USA; Judith Pérez-Velázquez, Alanna Hoyer-Leitzel, Bowdoin College, Tapovan Lolla and Pierre Lermusiaux, Helmholtz Zentrum München, Germany; USA Massachusetts Institute of Technology, USA Zahra Aminzare, Rutgers University, USA; Alexandria Volkening, Brown University, USA 36 2015 SIAM Conference on Applications of Dynamical Systems

Monday, May 18 Monday, May 18 Monday, May 18 MS39 MS40 MS41 Reduced Dynamical The Behavior of Renewable Energy Models and Their Autonomous Agents in and Power Grids: Applications - Part I of II Diverse Applications Their Mathematical 1:15 PM-3:15 PM 1:15 PM-3:15 PM Characterizations - Part I of II Room:Maybird Room:Superior A 1:15 PM-3:15 PM For Part 2 see MS52 Many different applications, such as the Room:Superior B The purpose is to present a cross-section of swarming of insects, the interaction of For Part 2 see MS54 leading-edge research on the development, cells, and the flow of traffic, when studied It is our social demand to introduce more analysis, numerical solution, visualization mathematically, naturally take the form renewable energy resources into power grids. and applications of reduced dynamical of agent-based models. The diversity of However, because renewable energy outputs systems models. These models may arise perspectives on the behavior of autonomous fluctuate according to weather conditions, via simplification of form of infinite- agents across these fields provides an we need to control and/or optimize power dimensional systems, reduction in cardinality opportunity for a cross-fertilization of grids so that we can keep the voltage and of the dimension, possibly by restriction ideas and techniques. The goal of this frequency as constant and stable. Here we to invariant submanifolds, and ad hoc minisymposium is to capitalize on the put together some recent advances to achieve techniques based upon focusing on certain differences between these applications, in this need mathematically. This need for more combinations of variables. Among the the context of agent-based models and their renewables makes us to combine several fields reductions to be discussed are simplified analyses, to ignite more ideas and better of mathematics together such as dynamical infinite-dimensional models for granular answer the questions that arise in many systems theory, control theory and complex flows, reduced dimensional models via fields. network theory. This need also brings us into extensions of the zero derivative principle, Organizer: Paul A. Carter new research directions, which will turn our discrete dynamical systems reductions for Brown University, USA mathematical tools more practical. logical circuits and ecological models, and discrete integrable reductions of continuum Organizer: Alexandria Volkening Organizer: Yoshito Hirata models. Brown University, USA University of Tokyo, Japan Organizer: Denis Blackmore 1:15-1:40 Modeling Stripe Formation Organizer: Jun-ichi Imura New Jersey Institute of Technology, in Zebrafish Tokyo Institute of Technology, Japan USA Alexandria Volkening and Bjorn Organizer: Juergen Kurths Sandstede, Brown University, USA Organizer: Anthony Rosato Potsdam Institute for Climate Impact New Jersey Institute of Technology, 1:45-2:10 Predator-Swarm Research and Humboldt University Interactions USA Berlin, Germany Theodore Kolokolnikov, Dalhousie 1:15-1:40 Time Series Prediction for 1:15-1:40 Reduced Models for University, Canada Granular and Ecological Dynamics Renewable Energy Resources Denis Blackmore, Anthony Rosato, 2:15-2:40 Non-Standard Travelling Yoshito Hirata, University of Tokyo, Japan; and Hao Wu, New Jersey Institute of Waves in Traffic and Pedestrian Flow Kazuyuki Aihara, JST/University of Tokyo, Models Technology, USA Japan; Hideyuki Suzuki, University of Paul Carter, Brown University, USA; Peter Tokyo, Japan 1:45-2:10 On the Calogero Type Leth Christiansen, Technical University 1:45-2:10 Analysis of Systems in Integrable Discretization of Nonlinear of Denmark, Denmark; Yuri Gaididei, Buildings Using Koopman Operator Dynamical Systems Bogolyubov Institute for Theoretical Methods Anatolij Prykarpatski, AGH University of Physics, Ukraine; Carlos Gorria, Science and Technology, Poland University of the Basque Country, Spain; Michael Georgescu, University of California, Santa Barbara, USA 2:15-2:40 A Scheme for Modeling Christian Marschler, Technical University and Analyzing the Dynamics of of Denmark, Denmark; Bjorn Sandstede, Logical Circuits Brown University, USA; Mads Peter Aminur Rahman, New Jersey Institute of Soerensen and Jens Starke, Technical Technology, USA University of Denmark, Denmark 2:45-3:10 Collective Coordinates as 2:45-3:10 Topological Data Analysis Model Reduction for Nonlinear Wave of Biological Aggregation Models Interactions Chad M. Topaz, Lori Ziegelmeier, and Tom Ivan C. Christov, Los Alamos National Halverson, Macalester College, USA Laboratory, USA continued on next page 2015 SIAM Conference on Applications of Dynamical Systems 37

2:15-2:40 Hierarchical Subsystem Monday, May 18 Monday, May 18 Clustering for Distributed Control of Networked Systems MS42 MS43 Tomonori Sadamoto, Takayuki Ishizaki, and Jun-ichi Imura, Tokyo Institute of Extensions and Applications Applications of Exactly Technology, Japan of Dynamic Mode Solvable Chaos 2:45-3:10 Stability of Power Grid: Decomposition - Part I of II 1:15 PM-3:15 PM Dynamical Systems Perspective Andrej Gajduk, Macedonian Academy of 1:15 PM-3:15 PM Room:Primrose A Sciences and Arts, Macedonia; Mirko Room:White Pine Recent work on certain hybrid dynamical Todorovski, Saints Cyril and Methodius For Part 2 see MS55 systems, containing linear continuous-time University of Skopje, Macedonia; Lasko Dynamic mode decomposition (DMD) differential equations coupled to a discrete- Basnarkov, Macedonian Academy of is a powerful method that identifies time switching condition, revealed a new class Sciences and Arts, Macedonia; Ljupco spatial-temporal coherent structures in of chaos that exhibits a quasi-linear nature. Kocarev, University of California, San high-dimensional datasets. Introduced These systems generate chaotic waveforms as Diego, USA less than a decade ago, it has quickly typical solutions that have an exact analytic gained a wide following due to its ease of description as a linear convolution of a fixed implementation and broad applicability. In basis function and a symbolic dynamics. this minisymposium, we present exciting As a consequence, for the first time, chaotic new extensions and applications of waveforms could be dissected and analyzed DMD. These include theoretical advances using the tools of linear analysis. This in rigorously defining DMD and its minisymposium explores physical and connections to Koopman operator theory, technological applications of exactly solvable as well as applications in fluid mechanics, chaotic oscillators. neuroscience, and epidemiology. We also Organizer: Lucas Illing introduce algorithmic enhancements that Reed College, USA account for the effects of control inputs, correct for noise, and enable ever-larger Organizer: Ned J. Corron computations, for instance using compressive US Army RDECOM, USA sensing. 1:15-1:40 Communication Waveforms Organizer: Jonathan H. Tu and Exactly Solvable Chaos University of California, Berkeley, USA Ned J. Corron and Jonathan N. Blakely, US Army RDECOM, USA Organizer: Steven Brunton 1:45-2:10 A Pseudo-Matched Filter for University of Washington, USA Solvable Chaos 1:15-1:40 A Rigorous Definition Seth D. Cohen, Miltec Corp., USA and Theory of Dynamic Mode Decomposition 2:15-2:40 Methods for Implementing Exactly Solvable Chaos in Electronic Jonathan H. Tu, University of California, Circuits Berkeley, USA; Clarence Rowley, Princeton University, USA Aubrey N. Beal and Robert Dean, Auburn University, USA 1:45-2:10 On the Relationship Between Koopman Mode 2:45-3:10 Exactly Solvable Chaos in Decomposition and Dynamic Mode An Electromechanical Oscillator Decomposition Lucas Illing, Reed College, USA Hassan Arbabi and Igor Mezic, University of California, Santa Barbara, USA 2:15-2:40 Dynamic Mode Decomposition with Control with a Special Focus on Epidemiological Applications Joshua L. Proctor, Intellectual Ventures, USA 2:45-3:10 Extracting Spatial-Temporal Coherent Patterns in Large-Scale Neural Recordings Using Dynamic Mode Decomposition Bing W. Brunton, University of Washington, USA 38 2015 SIAM Conference on Applications of Dynamical Systems

Monday, May 18 Monday, May 18 Monday, May 18 MS44 CP14 CP15 Recent Advances in Topics in Fluids Topics in Noisy/Stochastic/ Ergodic Theory with an Eye 3:45 PM-4:45 PM Random Dynamical to Applications Room:Ballroom I Systems 1:15 PM-3:15 PM Chair: Robert E. Ecke, Los Alamos 3:45 PM-5:45 PM Room:Primrose B National Laboratory, USA Room:Ballroom II Many modelling approaches in applied 3:45-4:00 Reduced Modeling of Exact Chair: Kevin Lin, University of Arizona, dynamical systems rely either directly, Coherent States in Shear Flow USA or indirectly on theoretical results from Cedric Beaume, Imperial College London, 3:45-4:00 Embedology for Control United Kingdom; Greg Chini, University ergodic theory. Ergodic theory can and Random Dynamical Systems provide a framework for the modelling of New Hampshire, USA; Keith Julien, Boumediene Hamzi, Imperial College process by guiding us to make productive University of Colorado Boulder, USA; London, United Kingdom; Jake Bouvrie, simplifications to the model and/or can Edgar Knobloch, University of California, Massachusetts Institute of Technology, suggest directions in which to study a Berkeley, USA USA given model (e.g. invariants, exponents, 4:05-4:20 Effects of Fluid Dynamics correlations, and their rates of decay, almost on Experiments with Compressed/ 4:05-4:20 Noise Shaping and Pattern invariant states and so-on) or more directly, Expanded Surfactant Monolayers Discrimination in Recurrent Spiking Neuronal Networks through numerical implementation of Maria Higuera, Jose Perales, and Jose theoretical results, either in an experimental Vega, Universidad Politécnica de Madrid, Hermann Riecke, Tom Zhao, and Siu Fai or a rigorous context. This minisymposium Spain Chow, Northwestern University, USA will provide a sample from the range of 4:25-4:40 Faster Sensitivity Estimates recent contributions to applications and 4:25-4:40 Stratified Shear Turbulence Experiments for Stochastic Differential Equations theoretical advances in the field, the latter, Kevin K. Lin, University of Arizona, USA; ‘with an eye to applications’. Robert E. Ecke, Los Alamos National Laboratory, USA; Philippe Odier, ENS Jonathan C. Mattingly, Duke University, Organizer: Chris Bose Lyon, France USA University of Victoria, Canada 4:45-5:00 Zero Density of Open 1:15-1:40 Rigorous Numerical Paths in the Lorentz Mirror Model for Approximation of Invariant Measures Arbitrary Mirror Probability -- History and Recent Progress David P. Sanders, National University Chris Bose, University of Victoria, Canada of Mexico, Mexico; Atahualpa Kraemer, Heinrich-Heine Universitaet Duesseldorf, 1:45-2:10 A Measurable Perspective Germany on Finite Time Coherence Erik Bollt and Tian Ma, Clarkson 5:05-5:20 Power System Stochastic University, USA Modeling Mathew Titus, Yue Zhang, and Eduardo 2:15-2:40 Non-Autonomous Cotilla-Sanchez, Oregon State University, Dynamical Systems, Multiplicative USA Ergodic Theorems and Applications Cecilia Gonzalez Tokman and Gary 5:25-5:40 Noisy-Bar Problem Froyland, University of New South Wales, Korana Burke, University of California, Australia; Anthony Quas, University of Davis, USA Victoria, Canada 2:45-3:10 On Triangularization of Matrix Cocycles in the Multiplicative Ergodic Theorem Joseph Horan, University of Victoria, Canada

Coffee Break 3:15 PM-3:45 PM Room:Golden Cliff 2015 SIAM Conference on Applications of Dynamical Systems 39

Monday, May 18 Monday, May 18 Monday, May 18 CP16 CP17 CP18 Topics in Networks II Topics in Computational Topics in Complex Systems 3:45 PM-5:25 PM Dynamical Systems II 3:45 PM-5:45 PM Room:Ballroom III 3:45 PM-5:45 PM Room:Magpie B Chair: Renate A. Wackerbauer, Room:Magpie A Chair: Steven H. Strogatz, Cornell University of Alaska, Fairbanks, USA Chair: James D. Meiss, University of University, USA 3:45-4:00 Control of Stochastic and Colorado Boulder, USA 3:45-4:00 Dynamics of Correlated Induced Switching in Biophysical 3:45-4:00 The Existence of Horseshoe Novelties Complex Networks Dynamics in Three Dimensional Steven H. Strogatz, Cornell University, Daniel Wells, William Kath, and Adilson E. Lotka-Volterra Systems USA Motter, Northwestern University, USA Rizgar Salih and Colin Christopher, 4:05-4:20 Hysteresis Effects in 4:05-4:20 Effects of Network Plymouth University, United Kingdom Pedestrian Flows Structure on the Synchronization of 4:05-4:20 Invariant Manifolds Poul G. Hjorth and Jens Starke, Technical Hamiltonian Systems and Space Mission Design in the University of Denmark, Denmark Yogesh Virkar, Juan G. Restrepo, and Restricted Four-Body Problem 4:25-4:40 Robustness of Nonlinear James D. Meiss, University of Colorado Kaori Onozaki and Hiroaki Yoshimura, Models Boulder, USA Waseda University, Japan Fabio Della Rossa, Alessandro Colombo, 4:25-4:40 Transient Spatiotemporal 4:25-4:40 Efficient Kernel Algorithm for Fabio Dercole, and Carlo Piccardi, Chaos in a Network of Coupled the Dynamic Mode Decomposition of Politecnico di Milano, Italy Morris-Lecar Neurons Observed Data 4:45-5:00 Systems with Hidden Slow Renate A. Wackerbauer and Jacopo Wataru Kurebayashi, Sho Shirasaka, Fast Dynamics Lafranceschina, University of Alaska, and Hiroya Nakao, Tokyo Institute of Peter Szmolyan, Vienna University of Fairbanks, USA Technology, Japan Technology, Austria 4:45-5:00 Studies of Stable Manifolds 4:45-5:00 Perturbing the Cat Map: 5:05-5:20 A New Filter for State of a Spatially Extended Lattice Mixed Elliptic and Hyperbolic Estimation in Neural Mass Models Kuramoto Model Dynamics Dean R. Freestone, University of Andrea J. Welsh and Flavio Fenton, James D. Meiss, University of Colorado Melbourne, Melbourne, Australia & Georgia Institute of Technology, USA Boulder, USA; Lev Lerman, Lobachevsky Columbia University, New York, USA; 5:05-5:20 Consequence of Symmetry State University of Nizhny Novgorod, Philippa Karoly, Dragan Nesic, Mark Breaking in Two Coupled Kuramoto Russia Cook, and David Grayden, University of Networks 5:05-5:20 Classification of Critical Sets Melbourne, Australia Scott T. Watson, Ernest Barreto, Bernard and Images for Quadratic Maps of 5:25-5:40 Inferring Causal Structures Cotton, and Paul So, George Mason the Plane in Complex Systems Via Causation University, USA Bruce B. Peckham, University of Entropy Minnesota, Duluth, USA; Chia- Carlo Cafaro, Warren Lord, Jie Sun, and Hsing Nien, Providence University, Erik Bollt, Clarkson University, USA Taiwan; Richard McGehee, University of Minnesota, Duluth, USA; Bernd Krauskopf and Hinke M. Osinga, University of Auckland, New Zealand 5:25-5:40 Mixing on a Hemisphere Paul Park, Paul Umbanhowar, Julio Ottino, and Richard M. Lueptow, Northwestern University, USA 40 2015 SIAM Conference on Applications of Dynamical Systems

Monday, May 18 Monday, May 18 Monday, May 18 CP19 CP20 CP21 Topics in Classical Topics in Computational Topics in Biological Dynamical Systems Dynamical Systems & Dynamics III 3:45 PM-5:45 PM Pattern Formation 3:45 PM-5:25 PM Room:Wasatch A 3:45 PM-5:25 PM Room:Maybird Chair: Kelum D. Gajamannage, Room:Wasatch B Chair: Vladimir E. Bondarenko, Clarkson University, USA Chair: Mikheil Tutberidze, Ilia State Georgia State University, USA 3:45-4:00 New Asymptotics of University, Georgia 3:45-4:00 A Model of Heart Rate Homoclinic Orbits Near Bogdanov- 3:45-4:00 Nonlinear Behaviors As Dynamics for Changes in Exercise Takens Bifurcation Point Well As Bifurcation Mechanism in Intensity Bashir M. Al-Hdaibat and Willy Switched Dynamical Systems Michael J. Mazzoleni, Duke University, Govaerts, Ghent University, Belgium; Yu V. Wang, City College of New York, USA; Claudio Battaglini, University of Yuri Kuznetsov, University of Twente, USA North Carolina at Chapel Hill, USA; Brian Netherlands; Hil Meijer, Twente Mann, Duke University, USA University, Netherlands 4:05-4:20 Gpu-Based Computational Studies of the Interaction Between 4:05-4:20 The Evolutionary Dynamics 4:05-4:20 Metric Invariance Entropy Reentry Waves and Gap Junctional of Gamete Recognition Genes and Conditionally Invariant Measures Uncoupling in Cardiac Tissues David Mcavity and Mottet Geneva, Fritz Colonius, University of Augsburg, Zhihui Zhang, Florida State University, Evergreen State College, USA Germany USA 4:25-4:40 Β-Adrenergic Regulation 4:25-4:40 Periodic Orbit Theory of 4:25-4:40 On the Numerical of Action Potential and Calcium Continuous Media Integration of One Nonlinear Dynamics in a Model of Mouse Nazmi Burak Budanur and Predrag Parabolic Equation Ventricular Myocytes Cvitanovic, Georgia Institute of Mikheil Tutberidze, Ilia State University, Vladimir E. Bondarenko, Georgia State Technology, USA Georgia University, USA 4:45-5:00 A Dynamical and Algebraic 4:45-5:00 A Continuous Model for 4:45-5:00 Spike Time Dependent Study of a Family of Lienard the Pathfinding Problem with Self- Plasticity in a Spiking Neural Network Equations Transformable to Riccati Recovery Property Anushaya Mohapatra, Oregon State Equations Kei-Ichi Ueda, University of Toyama, University, USA; Mike Field and Chris Primitivo B. Acosta-Humanez, Jorge Japan; Masaaki Yadome and Yasumasa Bick, Rice University, USA Rodriguez-Contreras, and Alberto Nishiura, Tohoku University, Japan 5:05-5:20 A Mathematical Model Reyes-Linero, Universidad del Atlantico, 5:05-5:20 Patterns on Curved for Frog Population Dynamics with Colombia Backgrounds: the Influence of Local Batrachochydrium Dendrobatidis 5:05-5:20 Dimensionality Reduction Curvature on Pattern Formation (Bd) Infection of Collective Motion by Principal Frits Veerman and Philip K. Maini, Baoling Ma, University of Louisiana, Manifolds University of Oxford, United Kingdom Lafayette, USA Kelum D. Gajamannage, Clarkson University, USA; Sachit Butail, Indraprastha Institute of Information Technology Delhi, India; Maurizio Porfiri, Polytechnic Institute of New York University, USA; Erik Bollt, Clarkson University, USA 5:25-5:40 A Fast Explicit Method for Computing Invariant Solutions of High-Dimensional Dynamical Systems with Continuous Symmetries Mohammad Farazmand and Predrag Cvitanovic, Georgia Institute of Technology, USA 2015 SIAM Conference on Applications of Dynamical Systems 41

Monday, May 18 Monday, May 18 Monday, May 18 CP22 CP23 CP24 Delay Dynamical Systems & Topics in Optical and Topics in Wave Dynamics Time Series Analysis Related Systems 3:45 PM-5:25 PM 3:45 PM-5:05 PM 3:45 PM-5:45 PM Room:Primrose A Room:Superior A Room:Superior B Chair: Ibrahim Fatkullin, University of Chair: Sue Ann Campbell, University of Chair: Estathios Charalampidis, Arizona, USA Waterloo, Canada University of Massachusetts, USA 3:45-4:00 Coupled Parametrically 3:45-4:00 Plankton Models with Time 3:45-4:00 Control of Extreme Events Forced Oscillators and Modulated Delay in the Bubbling Onset of Wave Cross-Waves Sue Ann Campbell, Matt Kloosterman, and Turbulence in the Forced and Jeff Porter, Pablo Salgado Sanchez, Ignacio Francis Poulin, University of Waterloo, Damped Non-Linear Schrödinger Tinao, and Ana Laveron-Simavilla, Canada Equation Universidad Politécnica de Madrid, Spain Paulo Galuzio, Ricardo L. Viana, and 4:05-4:20 Stochastic Delay in Gene 4:05-4:20 Finding the Stokes Wave: Sergio R. Lopes, Federal University of Regulation: Exact Stability Analysis From Low Steepness to Almost Paraná, Brazil Limiting Wave Mehdi Sadeghpour and Gabor Orosz, University of Michigan, Ann Arbor, USA 4:05-4:20 Vector Rogue Waves and Sergey Dyachenko, University of Arizona, Dark-Bright Boomeronic Solitons in USA 4:25-4:40 Computational Topology Autonomous and Non-Autonomous Techniques for Characterizing Time 4:25-4:40 Singularities of the Stokes’ Settings Series Data Wave: Numerical Simulation Efstathios Charalampidis, University Elizabeth Bradley, James D. Meiss, and Alexander O. Korotkevich, University of of Massachusetts, Amherst, USA; R. Joshua T. Garland, University of Colorado New Mexico, USA BABU Mareeswaran and T. Kanna, Boulder, USA; Nicole Sanderson, Bishop Heber College, India; Panayotis 4:45-5:00 Branch Cut Singularity of University of Colorado, USA Kevrekidis, University of Massachusetts, Stokes Wave 4:45-5:00 Noise, Chaos and Entropy USA; Dimitri Frantzeskakis, University of Pavel M. Lushnikov, University of New Generation in a Time-Delayed Athens, Greece Mexico, USA Dynamical System 4:25-4:40 Reducibility of One- 5:05-5:20 Blow-Ups in Nonlinear Pdes, and Rajarshi Roy, Aaron M. Hagerstrom dimensional Quasi-periodic Composite Grid-Particle Methods, University of Maryland, USA; Thomas E. Schrödinger Equations and Stochastic Particle Systems Murphy, University of Maryland, College Jiansheng Geng, Nanjing University, China Ibrahim Fatkullin, University of Arizona, Park, USA USA 4:45-5:00 Numerical Continuation of Invariant Solutions of the Complex Ginzburg-Landau Equation Vanessa Lopez, IBM T.J. Watson Research Center, USA 5:05-5:20 Nonlinear Oscillations and Bifurcations in Silicon Photonic Resonators Alexander Slawik and Daniel Abrams, Northwestern University, USA 5:25-5:40 Noise and Determinism of Stimulated Brillouin Scattering Dynamics in Optical Fiber Diana A. Arroyo-Almanza, Rafael Setra, and Zetian Ni, University of Maryland, USA; Thomas E. Murphy, University of Maryland, College Park, USA; Rajarshi Roy, University of Maryland, USA 42 2015 SIAM Conference on Applications of Dynamical Systems

Monday, May 18 Monday, May 18 Monday, May 18 CP25 IP3 PD1 Topics in Classical and Fluid Filtering Partially Observed Journal Editors Panel and Dynamical Systems Chaotic Deterministic Reception (pizza and light 3:45 PM-5:25 PM Dynamical Systems refreshments available) Room:Primrose B 6:00 PM-6:45 PM 7:00 PM-8:00 PM Room:Ballroom Room:Ballroom Chair: To Be Determined 3:45-4:00 Experiments on a Pinball- Chair: Bjorn Sandstede, Brown Chair: Lora Billings, Montclair State Like Oscillator University, USA University, USA Lawrie N. Virgin, Duke University, USA This talk is concerned with determining Wondering where to submit your next 4:05-4:20 Jetting-BubblingTransition in the state of a chaotic dynamical system, for manuscript? What is the optimal journal for Microflows which the initial condition is only known publishing work? How does the editorial probabilisticlly, given partial and noisy process work? In this panel, editors of the Dipin S. Pillai and S. Pushpavanam, Indian observations. In particular it is of interest leading journals in the area of dynamical Institute of Technology Madras, India to study this problem in the limit of a systems will be making short presentations to 4:25-4:40 Exploring the Hyperbolicity large number of such observations, over inform potential authors and readers. Editors of Chaotic Rayleigh-Bénard a long time interval. A key question is to will describe the subject areas covered by their Convection determine which observations are sufficient journals, describe their acceptance criteria Mu Xu and Mark Paul, Virginia Tech, USA in order to accurately recover the signal, and and the editorial process they use to evaluate 4:45-5:00 Snakes on An Invariant thereby overcome the lack of predictability manuscripts, and will also present vital Plane: Coupled Translational- caused by sensitive dependence on initial statistics for their journals. As a collection, Rotational Dynamics of Flying Snakes conditions. A canonical application is journals in the field span a broad spectrum Isaac Yeaton, Hodjat Pendar, Jake Socha, the development of probabilistic weather with a tremendous variation in authors, and Shane D. Ross, Virginia Tech, USA forecasts. In order to study this problem audiences, traditions, and editorial practices. concretely, we will focus on a wide class One goal of this panel, a first of its kind, is to 5:05-5:20 Finding Model Parameters of dissipative differential equations with scope the publication landscape in dynamical Without Prior Knowledge of quadratic energy-conserving nonlinearity, systems. The presentations will be followed Solve-Able Regions: A Solar including the Navier-Stokes equation on a by a reception sponsored by the publishing Thermochemistry Case-Study two dimensional torus. The work presented companies. In this informal setting, editors Karl Schmitt, Luke Venstrom, William D. is contained in the paper D. Sanz-Alonso and will be available answer questions. Pizza and Arloff, and Leandro Jaime, Valparaiso A.M.Stuart, “Long-time asymptotics of the light refreshments will be served. University, USA filtering distribution for partially observed Panelists: chaotic deterministic dynamical systems” (http://arxiv.org/abs/1411.6510); see also Eli Ben-Naim the paper K.J.H. Law, A. Shukla and A.M. Los Alamos National Laboratory, USA - Intermission Stuart, “Analysis of the 3DVAR filter for Physical Review E, American Physical 5:45 PM-6:00 PM the partially observed Lorenz ‘63 model,’” Society Discrete and Continuous Dynamical David Campbell Systems A, 34(2014), and the book K.J.H. Boston University, USA - Chaos, American Law, A.M.Stuart and K. Zygalalkis, “Data Institute of Physics Assimilation: A Mathematical Introduction” (in preparation, 2015) for further background Serena Dalena references. Physical Review Letters, American Physical Society, USA Andrew Stuart Charles Doering University of Warwick, United Kingdom University of Michigan, USA - Physics Letters A, Elsevier Edgar Knobloch Intermission University of California, Berkeley, USA - 6:45 PM-7:00 PM Nonlinearity, Institute of Physics Joceline Lega University of Arizona, USA - Physica D, Elsevier Bjorn Sandstede Brown University, USA - SIAM Journal on Applied Dynamical Systems (SIADS) 2015 SIAM Conference on Applications of Dynamical Systems 43

Monday, May 18 Tuesday, May 19 Tuesday, May 19 SIAG/DS Business Meeting MS45 8:30 PM-9:30 PM Energy Transfer and Registration Room:Ballroom Harvesting in Nonlinear 8:00 AM-4:30 PM Complimentary wine and beer Systems - Part II of II will be served. Room:Ballroom Foyer 8:30 AM-10:30 AM Room:Ballroom I For Part 1 see MS32 The minisymposium will focus on recent developments and challenges related to energy transfer and harvesting in nonlinear systems. Special attention will be paid to rapidly developing research field of nonsmooth systems. Topics will include, but will not be limited to: • New results in the classical problem of divergent vs convergent heat conduction in models of atomic lattices; • Description of wave initiation, propagation and mitigation in granular systems; • Nonlinear targeted energy transfer in systems with strongly nonlinear attachments • Applications of strong and non-smooth nonlinearities for efficient energy harvesting. Organizer: Oleg Gendelman Technion Israel Institute of Technology, Israel Organizer: Alexander Vakakis University of Illinois, USA 8:30-8:55 Non-Linearizable Wave Equation: Nonlinear Sonic Vacuum Leonid Manevich, Russian Academy of Sciences, Russia; Alexander Vakakis, University of Illinois, USA 9:00-9:25 Vibration Energy Harvesting Based on Nonlinear Targeted Energy Transfer Kevin Remick, University of Illinois at Urbana-Champaign, USA; D Dane Quinn, University of Akron, USA; D. Michael McFarland, University of Illinois, USA; Lawrence Bergman, University of Illinois at Urbana-Champaign, USA; Alexander Vakakis, University of Illinois, USA 9:30-9:55 Nonlinear Energy Harvesting in Granular Media Christopher Chong, ETH Zürich, Switzerland 10:00-10:25 2D Energy Channeling in the Locally Resonant Acoustic Metamaterials Yuli Starosvetsky and Kirill Vorotnikov, Technion - Israel Institute of Technology, Israel 44 2015 SIAM Conference on Applications of Dynamical Systems

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS46 MS47 MS48 Cellular Decision Making Koopman Operator Bridging the Gap Between Under Noise Techniques in Dynamical Observations and 8:30 AM-10:30 AM Systems: Theory and Idealized Modeling: A Practice - Part I of II Comprehensive Approach Room:Ballroom II to Weather and Climate Understanding how living cells make 8:30 AM-10:30 AM decisions based on environmental inputs is Room:Ballroom III Predictability one of the keys to understanding all living For Part 2 see MS60 8:30 AM-10:30 AM systems. In the past decade, the behavior Koopman operator is a linear infinite- of genetic circuits has been studied in great Room:Magpie A dimensional composition operator that can detail, both theoretically and experimentally. be defined for arbitrary nonlinear dynamical Many important climate and weather While most studies focused on the role of systems. It retains the full information of the phenomenon are difficult to predict because intrinsic noise, extrinsic noise has remained nonlinear state-space dynamics. Study of of abrupt transitions in behavior due to largely unexplored, even though it may its spectral properties provides an alternate noise and nonlinearity. Determining whether dramatically affect the behavior of these framework for dynamical systems analysis. noise and nonlinearity manifest themselves systems. Understanding the combined Recently, the spectral theory of Koopman as an organizing or random forcing has influence of intrinsic and extrinsic noise on operator has been extended to dissipative important consequences for model choice the stochastic dynamics of gene expression systems. This enabled numerous applications and subsequent mechanistic understanding should give us insight on how biochemical based on the so-called Koopman Mode and predictability. This minisymposium networks have evolved to both control and Expansion in fields as diverse as fluid is centered on a two-fold approach to exploit their fluctuating environment. mechanics, image processing and power grid addressing this issue. First, observational Organizer: Michael Assaf engineering. In this minisymposium, we aim data is used as a tool to identify the relevant Hebrew University of Jerusalem, Israel to present and discuss the current status of physical processes that are at the core of complex atmospheric systems. Second, 8:30-8:55 The Effect of Extrinsic Noise Koopman operator techniques in theory and practice of dynamical systems. the insights gained from observations are on Gene Regulation leveraged to create simple, but physically Michael Assaf, Hebrew University of Organizer: Igor Mezic unabridged representations of real-world Jerusalem, Israel University of California, Santa Barbara, atmospheric phenomenon. USA 9:00-9:25 Fundamental Limits to the Organizer: Juliana Dias Precision of Multicellular Sensing Organizer: Yoshihiko Susuki NOAA Earth System Research Andrew Mugler, Purdue University, Kyoto University, Japan Laboratory USA; Matthew Brennan, Johns Hopkins 8:30-8:55 Koopman Mode Expansion University, USA; Andre Levchenko, Yale 8:30-8:55 An Observational Basis in Theory and Practice University, USA; Ilya Nemenman, Emory for Sudden Stratospheric Warmings University, USA Igor Mezic, University of California, Santa As Bifurcations in Planetary Wave Barbara, USA Amplitude 9:30-9:55 Inferring Predictive Signal- 9:00-9:25 What Can the Koopman John R. Albers, University of Colorado, Activated Gene Regulation Models USA from Noisy Single-Cell Data Operator Do for Dynamical Systems? Brian Munsky, Colorado State University, Rainer Nagel, University of Tübingen, 9:00-9:25 The Role of Noise in USA Germany Bifurcations in Fluids and the 9:30-9:55 Generalized Laplace Atmosphere 10:00-10:25 Coarse-Graining Yuzuru Sato, Hokkaido University, Japan; Biochemical Networks Analysis and Spaces of Observables for the Koopman Operator David J. Albers, Columbia University, Nikolai Sinitsyn, Los Alamos National USA Laboratory, USA Ryan Mohr, University of California, Santa Barbara, USA 9:30-9:55 Tropical-Extratropical Wave 10:00-10:25 Computation of the Interactions in the Atmosphere Koopman Eigenfunctions Is a Juliana Dias, NOAA Earth System Systematic Method for Global Research Laboratory Stability Analysis 10:00-10:25 The Use of Green Alexandre Mauroy, University of Liege, Functions of the Shallow Water Model Belgium; Igor Mezic, University of for Understanding Climate Anomalies California, Santa Barbara, USA Pedro Leite da Silva Dias, University of Sao Paulo, Brazil 2015 SIAM Conference on Applications of Dynamical Systems 45

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS49 MS50 MS51 Theory and Applications of Multistability in Biological Mechanisms for Nonsmooth Dynamics in Circuits: Theory and Computations in Neuronal Physical Systems - Part II of II Applications Networks 8:30 AM-10:00 AM 8:30 AM-10:00 AM 8:30 AM-10:30 AM Room:Magpie B Room:Wasatch A Room:Wasatch B For Part 1 see MS36 Complex networks facilitate the existence Our speakers address a range of neural This minisymposium will provide a mix of of multiple coexisting stable states in the network mechanisms in order to understand talks featuring theoretical developments in network dynamics. This is most prominent their impact on specific computations, nonsmooth systems as well as talks featuring in biological, gene, and neural networks including: synchrony detection through applications with nonsmooth dynamics. In that derive their functional flexibility from phase-delayed inhibition, olfactory coding either case, physical applications provide a high multiplicity of operational modes. using time-varying oscillations, and transfer the motivation for mathematical exploration. Robustness and multiplicity as well as the of correlations through convergent network Additionally, the minisymposium will blend transition dynamics is determined by network motifs. talks appropriate for a broad audiences and symmetry, structure and node dynamics. Organizer: Andrea K. Barreiro talks geared at experts. To that point, the The struggle of understanding such complex Southern Methodist University, USA minisymposium will begin with the very network dynamics has inspired novel general “How nonsmooth are the Earth mathematical approaches and continues Organizer: Pamela B. Fuller sciences?” which will set the stage for the to uncover fascinating mechanisms of real Rensselaer Polytechnic Institute, USA rest of the speakers. Other talks will discuss network function. The speakers in this session 8:30-8:55 Impact of Single-Neuron issues such as generalized bifurcations, will present novel mathematical problems Dynamics on Transfer of Correlations canard phenomena, synchronization, and the of understanding dynamical transitions on from Common Input new area of resilience. complex biological networks. Andrea K. Barreiro, Southern Methodist Organizer: Andrew Roberts Organizer: Marcos Rodriguez University, USA Cornell University, USA Centro Universitario De La Defensa 9:00-9:25 Integrate-and-Fire Model of Organizer: Esther Widiasih Zaragoza, Spain Insect Olfaction University of Hawaii, West Oahu, USA Organizer: Justus T. Schwabedal Pamela B. Fuller and Gregor Kovacic, Rensselaer Polytechnic Institute, 8:30-8:55 Canard Phenomena in Georgia State University, USA USA; David Cai, Shanghai Jiao Tong Nonsmooth Systems 8:30-8:55 From Andronov-Hopf to Z_3 University, China and Courant Institute Andrew Roberts, Cornell University, USA Heteroclinic Bifurcations in Cpgs of Mathematical Sciences, New York 9:00-9:25 Generalized Hopf Marcos Rodriguez, Centro Universitario University, USA Bifurcation in a Nonsmooth Climte De La Defensa Zaragoza, Spain; Roberto 9:30-9:55 A Network of Excitatory and Model Barrio and Sergio Serrano, University Inhibitory Neurons with Gap Junctions Julie Leifeld, University of Minnesota, of Zaragoza, Spain; Andrey Shilnikov, Jennifer Kile and Gregor Kovacic, USA Georgia State University, USA Rensselaer Polytechnic Institute, 9:30-9:55 Dangerous Border Collision 9:00-9:25 Intrinsic Mechanisms for USA; David Cai, Shanghai Jiao Tong Pattern Generation in Three-Node Bifurcation in Piecewise Smooth Maps University, China and Courant Institute Networks Soumitro Banerjee and Arindam Saha, of Mathematical Sciences, New York Indian Institute for Science Education and Jarod Collens, Aaron Kelley, Deniz Alacam, University, USA Research, Kolkata, India; Viktor Avrutin, Tingli Xing, Drake Knapper, Justus 10:00-10:25 Phase Delayed Inhibition University of Stuttgart, Germany; Laura T. Schwabedal, and Andrey Shilnikov, Georgia State University, USA and the Representation of Whisker Gardini, University of Urbino, Italy Deflection Velocity in the Rodent 9:30-9:55 Key Bifurcations of Bursting Barrel Cortex Polyrhythms in 3-Cell Central Pattern Mainak Patel, College of William & Mary, Generators USA; Runjing Liu, Duke University, USA; Jeremy Wojcik, Applied Technology Badal Joshi, California State University, Associates, USA; Robert Clewley, Justus San Marcos, USA T. Schwabedal, and Andrey Shilnikov, Georgia State University, USA 46 2015 SIAM Conference on Applications of Dynamical Systems

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS52 MS53 MS54 Reduced Dynamical Models Ostwald Ripening, Renewable Energy and Power and Their Applications - Part Aggregate Growth and Grids: Their Mathematical II of II Precipitation Characterizations - 8:30 AM-10:30 AM 8:30 AM-10:30 AM Part II of II Room:Maybird Room:Superior A 8:30 AM-10:00 AM For Part 1 see MS39 The minisymposium will address new Room:Superior B The purpose is to present a cross-section of developments on the impact of fluctuations For Part 1 see MS41 leading-edge research on the development, of the environment on aggregate growth and It is our social demand to introduce more analysis, numerical solution, visualization the emergence of precipitation. There will renewable energy resources into power grids. and applications of reduced dynamical comprise two times two talks. There will However, because renewable energy outputs systems models. These models may arise via be two talks addressing recent theoretical fluctuate according to weather conditions, simplification of form of infinite-dimensional progress focusing on Ostwald ripening and we need to control and/or optimize power systems, reduction in cardinality of the the crossover to a runaway growth leading to grids so that we can keep the voltage and dimension, possibly by restriction to invariant precipitation, respectively. Another two talks, frequency as constant and stable. Here we submanifolds, and ad hoc techniques based will address recent advances in applications, put together some recent advances to achieve upon focusing on certain combinations nanoparticle synthesis and steel production. this need mathematically. This need for more of variables. Among the reductions to be Organizer: Jürgen Vollmer renewables makes us to combine several fields discussed are simplified infinite-dimensional Max Planck Institute for Dynamics and of mathematics together such as dynamical models for granular flows, reduced Self-Organization, Germany systems theory, control theory and complex dimensional models via extensions of the network theory. This need also brings us into zero derivative principle, discrete dynamical 8:30-8:55 Episodic Precipitaton new research directions, which will turn our systems reductions for logical circuits and Jürgen Vollmer, Max Planck Institute mathematical tools more practical. ecological models, and discrete integrable for Dynamics and Self-Organization, reductions of continuum models. Germany Organizer: Yoshito Hirata University of Tokyo, Japan Organizer: Denis Blackmore 9:00-9:25 Ostwald Ripening and New Jersey Institute of Technology, USA Nanoparticle Growth Organizer: Jun-ichi Imura Martin Rohloff, Max Planck Institute Tokyo Institute of Technology, Japan Organizer: Anthony Rosato for Dynamics and Self-Organization, New Jersey Institute of Technology, USA Organizer: Juergen Kurths Germany Potsdam Institute for Climate Impact 8:30-8:55 Idealized Models for Vortex 9:30-9:55 Aggregate Growth in Research and Humboldt University Shedding and Fluid-Body Interactions Optimizing Steel Production Berlin, Germany Scott D. Kelly, University of Illinois at Nikolas Rimbert, Université de Lorraine, Urbana-Champaign, USA 8:30-8:55 Basin Stability for Evaluating France Large Perturbations in Power Grids 9:00-9:25 A Novel Semidiscete 10:00-10:25 Initiation of Rain and Juergen Kurths, Potsdam Institute for Scheme for a Reduced Continuum Inertial Particles Climate Impact Research and Humboldt Flow Model Markus Abel, University of Potsdam, University Berlin, Germany Hao Wu and Denis Blackmore, New Jersey Germany Institute of Technology, USA 9:00-9:25 Model Free Tuning of Wind Farms for Maximizing Power 9:30-9:55 Visualization of Reduced Production Granular Dynamics Mohd Ashraf Ahmad, Shun-Ichi Azuma, Xavier M. Tricoche, Purdue University, and Toshiharu Sugie, Kyoto University, USA Japan 10:00-10:25 Extending the Zero 9:30-9:55 Predicting Critical Links in Derivative Principle Complex Supply Networks Morten Brons, Technical University Marc Timme, Max-Planck-Institute for of Denmark, Denmark; Eric Benoît, Dynamics and Self-Organization, Germany; Universitè de la Rochelle, France; Mathieu Dirk Witthaut, Forschungszentrum Jülich, Desroches and Maciej Krupa, INRIA Germany; Martin Rohden, University of Paris-Rocquencourt, France Bremen, Germany; Xiaozhu Zhang and Sarah Hallerberg, Max Planck Institute for Dynamics and Self-Organization, Germany 2015 SIAM Conference on Applications of Dynamical Systems 47

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS55 MS56 MS57 Extensions and Applications Topology and Computation Chaos and Strange of Dynamic Mode in Dynamics Attractors Decomposition - Part II of II 8:30 AM-10:30 AM 8:30 AM-10:30 AM 8:30 AM-10:30 AM Room:Primrose A Room:Primrose B Room:White Pine Classical Morse theory provides a direct The purpose of this minisymposium is to For Part 1 see MS42 link between the topology of a manifold discuss the state of the art in the modern Dynamic mode decomposition (DMD) and gradient dynamics on it. Extensions chaos theory and applications of the theory is a powerful method that identifies of Morse-theoretic ideas due to Conley (in to problems in biology, chemistry, mechanics spatial-temporal coherent structures in the finite dimensional setting) and Floer (in etc. high-dimensional datasets. Introduced the infinite dimensional cases) are powerful Organizer: Ivan Ovsyannikov topological tools in applied dynamical less than a decade ago, it has quickly University of Bremen, Germany gained a wide following due to its ease of systems. In particular, the associated 8:30-8:55 Global Invariant Manifolds implementation and broad applicability. In homology provides computable invariants Unravelling Shilnikov Chaos this minisymposium, we present exciting of dynamical systems. This homology is new extensions and applications of thus well-suited for numerical approaches Pablo Aguirre, Universidad Técnica DMD. These include theoretical advances to understanding global dynamics. This Federico Santa María, Chile; Bernd in rigorously defining DMD and its minisymposium explores recent advances Krauskopf and Hinke M. Osinga, connections to Koopman operator theory, in finite and infinite dimensional dynamical University of Auckland, New Zealand as well as applications in fluid mechanics, systems using Morse-Conley-Floer index 9:00-9:25 Analytic Proof of Lorenz neuroscience, and epidemiology. We also techniques, rigorous computational Attractors in Flows and Maps introduce algorithmic enhancements that dynamics, ‘database’ explorations based Ivan Ovsyannikov, University of Bremen, account for the effects of control inputs, on Conley-Morse graphs, and topological Germany correct for noise, and enable ever-larger reconstruction from data. 9:30-9:55 The Lorenz System Near the computations, for instance using compressive Organizer: Jan Bouwe Van Den Loss of the Foliation Condition sensing. Berg Jennifer L. Creaser, Bernd Krauskopf, and Organizer: Jonathan H. Tu VU University, Amsterdam, Netherlands Hinke M. Osinga, University of Auckland, University of California, Berkeley, USA Organizer: Robert Vandervorst New Zealand Organizer: Steven Brunton VU University, Amsterdam, Netherlands 10:00-10:25 The Many Facets of Chaos University of Washington, USA 8:30-8:55 Rigorous Computing in Evelyn Sander, George Mason University, 8:30-8:55 Using Dynamic Mode Strongly Indefinite Problems USA Decomposition to Extract Linear Jean-Philippe Lessard, Université Laval, Global Modes from Nonlinear Fluid Canada; Jan Bouwe Van Den Berg and Robert Vandervorst, VU University, Flow Solvers Coffee Break Kunihiko Taira and Aditya Nair, Florida Amsterdam, Netherlands; Marcio State University, USA; Shervin Bagheri, Gameiro, University of Sao Paulo, Brazil 10:30 AM-11:00 AM KTH Royal Institute of Technology, 9:00-9:25 Computing Conley-Morse Room:Golden Cliff Sweden Databases 9:00-9:25 Improving the Accuracy of Shaun Harker, Rutgers University, USA Dynamic Mode Decomposition in the 9:30-9:55 Reconstructing Functions Presence of Noise from Dense Samples Scott Dawson, Maziar S. Hemati, Matthew Vidit Nanda, University of Pennsylvania, O. Williams, and Clarence Rowley, USA Princeton University, USA 10:00-10:25 Morse Homology on 9:30-9:55 Parallel Qr Algorithm Spaces of Braids for Data-Driven Decompositions, Patrick Hafkenscheid, VU University, in Particular Dynamic Mode Amsterdam, Netherlands Decomposition Taraneh Sayadi, University of Illinois at Urbana-Champaign, USA; Peter Schmid, Imperial College London, United Kingdom 10:00-10:25 Compressive Sensing and Dynamic Mode Decomposition Steven Brunton, University of Washington, USA 48 2015 SIAM Conference on Applications of Dynamical Systems

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 IP4 PD2 MS58 Fields of Dreams: Modeling Funding Agency Panel Snapshot and Pullback and Analysis of Large Scale 12:00 PM-1:00 PM Attractors, a Framework Activity in the Brain Room:Ballroom for Understanding Nonautonomous Dissipative 11:00 AM-11:45 AM Chair: Igor Mezic, University of Dynamics Room:Ballroom California, Santa Barbara, USA Chair: Michael Ward, University of A panel of representatives from federal 1:30 PM-3:30 PM British Columbia, Canada funding agencies will discuss trends and Room:Ballroom I opportunities for research funding in the area With the advent of optogenetics and the of dynamical systems. Each will describe Snapshot attractors generalize strange ability to record large numbers of neurons their funding guidelines and deadlines, and attractors from autonomous to with high temporal resolution, there is provide information about the their particular nonautonomous dynamics. A snapshot now a great deal of interest in both the funding interests. attractor is a time-dependent object in the temporal and spatial activity of neurons phase space of an open system that is the in the brain. In this talk, I will discuss a Panelists: asymptotic locus of trajectories initialized number of old and new developments in the in the remote past. Pullback attractors Fariba Fahroo study of these nonlinear integro-differential in the deterministic setting and random Air Force Office of Scientific Research, USA equations and how they apply to some new attractors in the stochastic setting provide a biological findings. Topics that I will discuss Predrag Neskovic solid mathematical foundation to this loose include the role of noise on spatio-temporal Office of Naval Research, USA definition. Random dynamical systems activity, the interaction between extrinsic Massimo Ruzzene theory encompasses both deterministic and and intrinsic activity, interactions between National Science Foundation, Directorate for random forcing. The minisymposium will multiple spatial networks, and finally some Engineering, USA clarify the connections between snapshot and recent applications of Filippov theory to pullback attractors, and shed further light on discontinuous neural field models. Samuel Stanton their invariant measures as generalized SRB Army Research Office, USA Bard Ermentrout measures. Applications will include climate dynamics and coupled oscillators. University of Pittsburgh, USA Henry Warchall National Science Foundation, Division of Organizer: Michael Ghil Mathematical Sciences, USA Ecole Normale Superieure de Paris, France, and University of California, Los Angeles, USA Lunch Break Organizer: Tamas Tel 11:45 AM-1:30 PM Eötvös Loránd University, Hungary Attendees on their own 1:30-1:55 Random Attractors and How They Help Understand Climate Change and Variability Michael Ghil, Ecole Normale Superieure de Paris, France, and University of California, Los Angeles, USA 2:00-2:25 SRB Measures for Time- Dependent and Random Attractors Lai-Sang Young, Courant Institute of Mathematical Sciences, New York University, USA 2:30-2:55 Snapshot Attractors and the Transition to Extensive Chaos in Large Systems of Mean-Field Coupled Oscillators Edward Ott, Wai Lim Ku, and Michelle Girvan, University of Maryland, USA

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3:00-3:25 The Quantification of the Tuesday, May 19 Tuesday, May 19 Nonergodic Property Via Snapshot Attractors: An Application to a MS59 MS60 Conceptual Climate Model Gabor Drotos, Hungarian Academy Synchronization of Chaos Koopman Operator of Sciences, Hungary; Tamas Bodai, and its Applications - Techniques in Dynamical Universitat Hamburg, Germany; Tamas Part I of II Systems: Theory and Tel, Eötvös Loránd University, Hungary 1:30 PM-3:30 PM Practice - Part II of II Room:Ballroom II 1:30 PM-3:30 PM For Part 2 see MS72 Room:Ballroom III Many fundamental processes in nature For Part 1 see MS47 are based on synchronization of chaos. Koopman operator is a linear infinite- This phenomenon is universal, robust and dimensional composition operator that can it may also involve large population of be defined for arbitrary nonlinear dynamical active elements distributed over extensive systems. It retains the full information of the spatial regions. In this minisymposium nonlinear state-space dynamics. Study of theoretical and application issues related its spectral properties provides an alternate to this phenomenon will be considered. In framework for dynamical systems analysis. particular, we address the fundamental role Recently, the spectral theory of Koopman that this phenomenon has in the organization operator has been extended to dissipative of the collective movement, in neuroscience systems. This enabled numerous applications and in the development of scenarios that lead based on the so-called Koopman Mode to coexistence of ordered and disordered Expansion in fields as diverse as fluid states. mechanics, image processing and power grid Organizer: Elbert E. Macau engineering. In this minisymposium, we aim Laboratory for Computing and Applied to present and discuss the current status of Mathematics and Brazilian Institute for Koopman operator techniques in theory and Space Research, Brazil practice of dynamical systems. Organizer: Epaminondas Rosa Organizer: Igor Mezic Illinois State University, USA University of California, Santa Barbara, USA 1:30-1:55 Chimeras in Networks of Identically Coupled Mechanical Organizer: Yoshihiko Susuki Oscillators Kyoto University, Japan Rosangela Follmann, Daniel Abrams, 1:30-1:55 Approximating the and Adilson E. Motter, Northwestern Koopman Operator Using Extended University, USA Dynamic Mode Decomposition 2:00-2:25 Dynamics of Clustering in Clarence Rowley and Matthew O. Networks with Repulsive Interaction Williams, Princeton University, USA Michael A. Zaks, University of Potsdam, 2:00-2:25 Machine Learning and the Germany Koopman Operator: Algorithms and 2:30-2:55 Synchronization Properties Applications Related to Neighborhood Similarity in Matthew O. Williams, Princeton a Complex Network of Non-Identical University, USA Oscillators 2:30-2:55 Dynamic Mode Elbert E. Macau, Laboratory for Decomposition for Multi-Resolution Computing and Applied Mathematics and Analysis Brazilian Institute for Space Research, J. Nathan Kutz, University of Washington, Brazil; Celso Bernardo Freitas, Instituto USA Nacional de Pesquisas Espaciais, Brazil; Ricardo L. Viana, Federal University of 3:00-3:25 Koopman Operator Paraná, Brazil Techniques in Power Grid Analysis Yoshihiko Susuki, Kyoto University, Japan 3:00-3:25 Chimera States in Networks with Symmetry-Breaking Coupling Anna Zakharova, Institute of Theoretical Physics, Berlin, Germany; Marie Kapeller, Berlin Institute of Technology, Germany; Eckehard Schöll, Technische Universität Berlin, Germany 50 2015 SIAM Conference on Applications of Dynamical Systems

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS61 MS62 MS63 State and Parameter Dynamics of Applications of Ensemble Estimation for Complex Nanoelectromechanical Data Assimilation Methods Dynamical Systems Systems (NEMS) to Climate Processes 1:30 PM-3:30 PM 1:30 PM-3:00 PM 1:30 PM-3:30 PM Room:Magpie A Room:Magpie B Room:Wasatch A Using mathematical models to analyze and Nanoelectromechanical systems (NEMS) Data assimilation methods seek to improve predict real world dynamical processes are the latest step in miniaturizing electro- estimates from a predictive model by meets with the difficulty that often not all mechanical devices. Due to their scale, we combining them with observed data. Most state variables are easy to observe, and can now study new physical regimes as realistic applications, such as those used in adequate values of model parameters may be well as develop novel technologies. The climate modeling, involve an underlying (partly) unknown. To estimate unobserved minisymposium presents an overview of dynamical system which is nonlinear. Many variables and model parameters, various their rich nonlinear and pattern formation ensemble methods have been designed to identification methods have been devised, dynamics alongside new theoretical and handle this nonlinearity, and additionally, aiming to match the model output to some experimental advances. The talks will often provide an estimate of the uncertainty observed time. This may be considered a address systems consisting of single NEMS in the prediction via the ensemble spread. form of data assimilation, a term which devices as well as NEMS networks. This session will include applications of refers to incorporating observed data into Organizer: Korana Burke ensemble data assimilation methods to several aspects of the climate, including computer models of the observed system. University of California, Davis, USA The presentations of this minisymposium oceans, sea ice, and the ionosphere. will address theoretical issues, new concepts, 1:30-1:55 Intrinsic Computation in NEMS Organizer: Laura Slivinski and applications of state and parameter Woods Hole Oceanographic Institute, estimation techniques. Russell Hawkins, University of California, Davis, USA USA Organizer: Ulrich Parlitz 1:30-1:55 An Application of Max Planck Institute for Dynamics and 2:00-2:25 Control of Complex Diffusion in Networks of NEMS Lagrangian Data Assimilation to Self-Organization, Germany Katama Bay, Ma Jeff Emenheiser, University of California, Organizer: Henry D. Abarbanel Davis, USA; Mehran Mesbahi, University Laura Slivinski, Larry Pratt, and Irina University of California, San Diego, of Washington, USA; Raissa D’Souza, Rypina, Woods Hole Oceanographic USA University of California, Davis, USA Institute, USA Organizer: Jochen Bröcker 2:30-2:55 Phase Synchronization 2:00-2:25 Ensemble Inflation by University of Reading, United Kingdom Between Nanoelectromechanical Shadowing Techniques Thomas Bellsky, University of Maine, 1:30-1:55 What Is the Right Functional Oscillators Matt Matheny, California Institute of USA; Lewis Mitchell, University of for Variational Data Assimilation? Adelaide, Australia Jochen Bröcker, University of Reading, Technology, USA United Kingdom 2:30-2:55 Ionospheric Weather Forecasting Using the Letkf Scheme 2:00-2:25 Filtering Unstable Quadratic Juan Durazo, Arizona State University, Dissipative Systems USA Kody Law, King Abdullah University of Science & Technology (KAUST), Saudi 3:00-3:25 Predicting Flow Reversals in Arabia; Abhishek Shukla, Daniel Sanz- a Cfd Simulated Thermosyphon Using Data Assimilation Alonso, and Andrew Stuart, University of Warwick, United Kingdom Andrew Reagan, University of Vermont, USA 2:30-2:55 Time Delay Methods for Variational Data Assimilation Uriel I. Morone, University of California, San Diego, USA 3:00-3:25 Observability of Chaotic Lorenz-96 Systems Jan Schumann-Bischoff, Stefan Luther, and Ulrich Parlitz, Max Planck Institute for Dynamics and Self-Organization, Germany 2015 SIAM Conference on Applications of Dynamical Systems 51

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS64 MS65 MS66 Excitation Waves in Spiral and Scroll Waves Stochastic and Nonlinear Heterogeneous Cardiac Dynamics in Experiment Dynamics of Neuronal Tissue: Theory and and Simulations - Part I of II Networks - Part I of II Experiments 1:30 PM-3:30 PM 1:30 PM-3:30 PM 1:30 PM-3:30 PM Room:Maybird Room:Superior A Room:Wasatch B For Part 2 see MS73 For Part 2 see MS74 Spiral and scroll waves are nonlinear Coherent neural activity patterns have been In this minisymposium we plan to bring dissipative patterns occurring in 2- and implicated as a substrate of short term together experimentalists and theorist 3-dimensional excitable and oscillatory memory, spatial navigation, sensation, and interested on the initiation and control of media, where they act as organizing centers. motor skills. Understanding the mechanisms spiral waves in the cardiac system. From Important motivation to study spiral and that underlie this activity requires using the dynamical system perspective cardiac scroll waves dynamics is better control sophisticated mathematical methods to tissue can be considered as an excitable of cardiac re-entry underlying dangerous analyze nonlinear models of neuronal medium. Indeed, experiments have shown that arrhythmias and fatal fibrillation. Though, networks. Recent advances along these lines dynamics of cardiac excitation waves during the vortices become of increasing interest address the effects of stochasticity, spatial fibrillation is similar to dynamics of spiral of their own as regimes of self-organisation heterogeneity, delays, and modular structure waves in excitable media. This perspective and transition to chaos. Recent advances on the dynamics of neuronal networks. This is already bearing fruits in understanding in experimental, theoretical and computer session will feature talks on cutting-edge cardiac arrhythmias and its management. For simulation techniques brought the studies methods for analyzing stochastic neural field example new defibrillation methods have closer to practical applications than ever equations, balanced networks, and mean been proposed using low energy pulses to before. This minisymposium provides a field theories for spiking networks. eliminate spiral waves from heterogeneities in sampling of the current state of experimental Organizer: Zachary Kilpatrick the cardiac tissue. This minisymposium will and computer simulation research in this University of Houston, USA discuss some of the underlying theoretical field. issues and experimental challenges. Organizer: Jonathan D. Touboul Organizer: Irina Biktasheva Organizer: Shajahan Thamara Collège de France, France University of Liverpool, United Kunnathu Kingdom Organizer: Bard Ermentrout Max Planck Institute for Dynamics and University of Pittsburgh, USA Self-Organization, Germany 1:30-1:55 Anatomy Induced Drift of Reentrant Waves in Human Atrium 1:30-1:55 Finite Size Effects in 1:30-1:55 Controlling Spiral Wave Irina Biktasheva, University of Liverpool, Networks of Theta Neurons Dynamics in Cardiac Monolayers United Kingdom; Vadim N. Biktashev and Siwei Qiu and Carson C. Chow, National Using Far Field Pulses Sanjay R. Kharche, University of Exeter, Institutes of Health, USA Shajahan Thamara Kunnathu, Sebastian United Kingdom; Gunnar Seemann, Berg, Valentin Krinsky, and Stefan Luther, 2:00-2:25 Optimal Decision-Making in Karlsruhe Institute of Technology, a Changing Environment Max Planck Institute for Dynamics and Germany; Henggui Zhang, The University Self-Organization, Germany Alan Veliz-Cuba, University of Houston of Manchester, UK and Rice University, USA; Zachary 2:00-2:25 A Mechanism of Spiral Wave 2:00-2:25 Stabilized Wave Segments Kilpatrick and Krešimir Josic, University Unpinning and Its Implications for the in An Excitable Medium with a Phase of Houston, USA Treatment of Cardiac Arrhythmias with Wave at the Wave Back Periodic Far-Field Pacing 2:30-2:55 A Computational Model of Eberhard Bodenschatz and Vladimir Philip Bittihn, University of California, San the Influence of Depolarization Block Zykov, Max-Planck-Institute for Dynamics on Initiation of Seizure-like Activity Diego, USA; Anna Behrend and Stefan and Self-Organization, Germany Luther, Max Planck Institute for Dynamics Duane Nykamp, University of Minnesota, and Self-Organization, Germany 2:30-2:55 Use of Delay-Differential USA Equations in Cardiac Models 3:00-3:25 Traveling Waves in a 2:30-2:55 The Effects of Cardiac Elizabeth M. Cherry, Cornell University, Fibroblasts on Wave Propagation Laminar Neural Field Model of Visual USA; Ryan Thompson, Rochester Institute in Ventricular Tissue: Insights from Cortex of Technology, USA Numerical Studies of Mathematical Samuel R. Carroll, University of Utah, Models 3:00-3:25 Spiral Wave Activity in a USA; Paul C. Bressloff, University of Alok R. Nayak and Rahul Pandit, Indian Mixture of Resting and Oscillating Utah, USA and University of Oxford, Institute of Science, Bangalore, India Cardiomyocytes: Limitations on United Kingdom Biopacemaker Development 3:00-3:25 How to Control Spiral Philippe Comtois, Université de Montréal, Waves Using Weak Signals: A Few Canada Suggestions S Sridhar, Ghent University, Belgium 52 2015 SIAM Conference on Applications of Dynamical Systems

Tuesday, May 19 Tuesday, May 19 3:00-3:25 Synchronization and the problem of Targeting in Multilayer MS67 MS68 Networks Ricardo Gutierrez, Weizmann Institute Evolutionary Dynamics The Structure and Dynamics of Science, Israel; Irene Sendina and Constraints of Quickly of Multilayer Networks Nadal, Universidad Rey Juan Carlos, Mutating Pathogens Spain; Massimiliano Zanin, Technical 1:30 PM-3:30 PM University of Madrid, Spain; David Papo, 1:30 PM-3:30 PM Room:White Pine Universidad Politécnica de Madrid, Spain; Room:Superior B Up until recently, network theory was almost Stefano Boccaletti, CNR, Italy exclusively limited to networks in which Understanding the evolution of pathogens all components were treated on equivalent is an important topic in science. High footing. Only in the last years, taking reproduction rates, large populations, high advantage of the enhanced resolution in real mutation and recombination rates, etc. data sets, network scientists have directed are but some of the strategies pathogens their interest to the multiplex character of adopt to escape selection pressure (immune real-world systems, and explicitly considered response, drugs/therapies, etc.). Fast paced the time-varying and multilayer nature of technological advances are allowing more networks. We offer a series of talks on both and more high throughput experimental structural and dynamical organization of investigations, thus uncovering novel graphs made of diverse relationships (layers) biological phenomena and providing large between its constituents, and cover several high-quality datasets. The aim of this relevant issues, from a full redefinition of the minisymposium is to gather experts in the basic structural measures, to understanding field of application of dynamical systems to how the multilayer nature of the network theoretical evolutionary biology to assess affects processes and dynamics. determinants and constraints of rapidly evolving organisms in complex environments. Organizer: Stefano Boccaletti Organizer: Simone Bianco CNR, Italy IBM Research, USA Organizer: Regino Criado 1:30-1:55 Costs and Benefits of Universidad Rey Juan Carlos, Spain Mutational Robustness in Rna Viruses Organizer: Charo I. del Genio Simone Bianco, IBM Research, USA University of Warwick, United Kingdom 2:00-2:25 Thermodynamics and Organizer: Irene Sendina Nadal Statistical Mechanics of Viral Evolution Universidad Rey Juan Carlos, Spain Barbara Jones and James Kaufman, IBM Research, USA; Justin Lessler, Johns Organizer: Miguel Romance Hopkins Bloomberg School of Public Universidad Rey Juan Carlos, Spain Health, USA Organizer: Zhen Wang 2:30-2:55 The Acceleration of Kyushu University, Japan Evolutionary Spread by Long-Range 1:30-1:55 Characterizing the Structure Dispersal of Multilayer Networks Oskar Hallatschek, University of Regino Criado and Miguel Romance, California, Berkeley, USA Universidad Rey Juan Carlos, Spain 3:00-3:25 Evolutionary Dynamics of 2:00-2:25 Game and Diffusion Mutator Phenotypes in Changing Dynamics in Multilayer Networks Environments Zhen Wang, Kyushu University, Japan Oana Carja, University of Pennsylvania, USA 2:30-2:55 Synchronization in Time Varying Networks: the Non Commutative Case Charo I. del Genio, University of Warwick, United Kingdom

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Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS69 MS70 MS71 Applications of Chaotic, Recent Applications of Emerging Collective Patterns Stochastic and Multiscale Singular Perturbation Theory in Dynamic Swarms Dynamics - Part I of II 4:00 PM-6:00 PM 1:30 PM-3:30 PM 1:30 PM-3:30 PM Room:Ballroom I Room:Primrose A Room:Primrose B Swarming dynamics are characterized by the Chaotic, stochastic and multiscale processes For Part 2 see MS77 emergence of complex motion patterns from are common in many areas of contemporary Singularly perturbed dynamical systems arise simple interactions between individual agents. scientific applications, such as modeling in many applications; for example, whenever Understanding the mechanisms which drive in neuroscience, nonlinear optics, and there is a natural separation of time scales the formation of these highly coherent motion geosciences, among others. Key topics or a bifurcation that changes the underlying pattern can lead to key insights into many of modeling for complex systems will be structure of a system. Many techniques processes in biology, such as the growth and brought together in this interdisciplinary have been developed to study such systems. development in multi-cellular organisms, and session. Two speakers will communicate Geometric singular perturbation methods use the collective motion of animal groups. Such their recent work in multiscale modeling for properties of “geometric” dynamical objects an understanding should prove valuable for neuroscience and nonlinear optics. Two other such as invariant manifolds and foliations. the development of algorithms to generate participants will report their new findings in On the other hand, spectral techniques have collective motions in engineered systems. coarse-graining and response to stochastic been used to study transitions between This minisymposium will focus on recent perturbations of more general nonlinear linear operators that are posed on different advancements in biological swarming systems. spaces but are nevertheless “close’’. This dynamics, as well as the application of these methods to swarming systems in engineering. Organizer: Rafail Abramov minisymposium presents recent theoretical results for which singular perturbation theory University of Illinois, Chicago, USA Organizer: Klementyna plays a key role in the analysis. Szwaykowska Organizer: Ibrahim Fatkullin Organizer: Kelly Mcquighan Naval Research Laboratory, USA University of Arizona, USA Boston University, USA Organizer: Luis Mier-y-Teran 1:30-1:55 The Response of Statistical Johns Hopkins Bloomberg School of Averages to Small Stochastic Forcing Organizer: Hermen Jan Hupkes Public Health, USA Rafail Abramov, University of Illinois, University of Leiden, The Netherlands Chicago, USA Organizer: Peter van Heijster 4:00-4:25 Nonlocal Aggregation Models: A Primer of Swarm Equilibria 2:00-2:25 Is Our Sensing Queensland University of Technology, Andrew J. Bernoff, Harvey Mudd College, Compressed? Australia USA; Chad M. Topaz, Macalester College, Gregor Kovacic, Rensselaer Polytechnic 1:30-1:55 Travelling Waves for Fully USA Institute, USA Discretized Bistable Reaction-Diffusion Problems 4:30-4:55 Fire Ants Build, Morph, and 2:30-2:55 A Multiscale Method for Repair to Survive Floods Optical Responses of Nano Structures Hermen Jan Hupkes, University of Leiden, The Netherlands David Hu, Georgia Institute of Technology, Di Liu, Michigan State University, USA USA 3:00-3:25 Parareal Methods for Highly 2:00-2:25 Oscillatory Pulses in FitzHugh-Nagumo 5:00-5:25 Quantifying Collective Cell Oscillatory Dynamical Systems Migration During Cancer Progression Richard Tsai, University of Texas, Paul A. Carter and Bjorn Sandstede, Brown University, USA Rachel Lee, University of Maryland, College Houston, USA Park, USA; Haicen Yue and Wouter-Jan 2:30-2:55 Invariant Manifolds of Multi Rappel, University of California, San Interior Spike States for the Cahn- Diego, USA; Wolfgang Losert, University Hilliard Equation of Maryland, College Park, USA Peter W. Bates, Michigan State University, USA 5:30-5:55 Aggregate Behaviors of Heterogeneous, Delay-Coupled 3:00-3:25 Slow-Fast Factorization of Agents the Evans Function Via the Riccati Klementyna Szwaykowska, Naval Research Transformation in the Semi-Strong Laboratory, USA; Christoffer R. Heckman, Regime University of Colorado Boulder, USA; Luis Björn De Rijk and Arjen Doelman, Leiden Mier-y-Teran, Johns Hopkins Bloomberg University, Netherlands; Jens Rademacher, School of Public Health, USA; Ira B. University of Bremen, Germany Schwartz, Naval Research Laboratory, USA Coffee Break 3:30 PM-4:00 PM Room:Golden Cliff 54 2015 SIAM Conference on Applications of Dynamical Systems

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS72 MS73 MS74 Synchronization of Spiral and Scroll Waves Stochastic and Nonlinear Chaos, Chimera and Dynamics in Experiment Dynamics of Neuronal Neurosciences - Part II of II and Simulations - Part II of II Networks - Part II of II 4:00 PM-6:00 PM 4:00 PM-6:00 PM 4:00 PM-6:00 PM Room:Ballroom II Room:Maybird Room:Superior A For Part 1 see MS59 For Part 1 see MS65 For Part 1 see MS66 Many fundamental processes in nature Spiral and scroll waves are nonlinear Coherent neural activity patterns have been are based on synchronization of chaos. dissipative patterns occurring in 2- and implicated as a substrate of short term This phenomenon is universal, robust and 3-dimensional excitable and oscillatory memory, spatial navigation, sensation, and it may also involve large population of media, where they act as organizing centers. motor skills. Understanding the mechanisms active elements distributed over extensive Important motivation to study spiral and that underlie this activity requires using spatial regions. In this minisymposium scroll waves dynamics is better control sophisticated mathematical methods to theoretical and application issues related of cardiac re-entry underlying dangerous analyze nonlinear models of neuronal to this phenomenon will be considered. In arrhythmias and fatal fibrillation. Though, networks. Recent advances along these lines particular, we address the fundamental role the vortices become of increasing interest address the effects of stochasticity, spatial that this phenomenon has in the organization of their own as regimes of self-organisation heterogeneity, delays, and modular structure of the collective movement, in neuroscience and transition to chaos. Recent advances on the dynamics of neuronal networks. This and in the development of scenarios that lead in experimental, theoretical and computer session will feature talks on cutting-edge to coexistence of ordered and disordered simulation techniques brought the studies methods for analyzing stochastic neural field states. closer to practical applications than ever equations, balanced networks, and mean before. This minisymposium provides a field theories for spiking networks. Organizer: Elbert E. Macau sampling of the current state of experimental Organizer: Zachary Kilpatrick Laboratory for Computing and Applied and computer simulation research in this University of Houston, USA Mathematics and Brazilian Institute for field. Space Research, Brazil Organizer: Jonathan D. Touboul Organizer: Irina Biktasheva Collège de France, France Organizer: Epaminondas Rosa University of Liverpool, United Illinois State University, USA Kingdom Organizer: Bard Ermentrout 4:00-4:25 Nontrivial Collective 4:00-4:25 Crossover Collisions of University of Pittsburgh, USA Dynamics in Networks of Pulse Scroll Waves 4:00-4:25 Oscillations in Neuronal Coupled Oscillators Dennis Kupitz and Marcus Hauser, Otto- Networks Antonio Politi and Ekkehard Ullner, von-Guericke University, Magdenburg, Stefanos Folias, University of Alaska, University of Aberdeen, United Kingdom Germany Anchorage, USA 4:30-4:55 Effects of Reciprocal 4:30-4:55 Role of Small Sized 4:30-4:55 Dynamics of Networks with Inhibitory Coupling in Synchronous Heterogeneities in the Onset and Partially Symmetric Connectivity Neurons Perpetuation of Arrhythmias Matrices Epaminondas Rosa, Illinois State Alexander Panfilov, Arne Defauw, Nele Nicolas Brunel, University of Chicago, University, USA Vandersickel, and Peter Dawyndt, Ghent USA 5:00-5:25 Clustering, Malleability and University, Belgium 5:00-5:25 Assembling Collective Synchronization of Hodgkin-Huxley- 5:00-5:25 Effects of Substrate Activity in Neural Circuits Type Neurons Geometry on Spiral Wave Chirality Eric Shea-Brown, University of Sergio R. Lopes, Thiago de L. Prado, Thomas D. Quail, Alvin Shrier, and Leon Washington, USA Ricardo L. Viana, and José C. P. Coninck, Glass, McGill University, Canada Federal University of Paraná, Brazil; 5:30-5:55 On a Kinetic Fitzhugh- Juergen Kurths, Potsdam Institute for 5:30-5:55 Scroll Waves in Viscous Nagumo Equation Climate Impact Research and Humboldt Systems with Stokes Flow: Writing Cristobal Quininao, Laboratoire Jacques- University Berlin, Germany Filaments and Other New Tricks Louis Lions, France Oliver Steinbock, Florida State University, 5:30-5:55 Synchronization in a USA Cortical Multilayered Computational Model: A Simulation Study Antonio C. Roque, Renan O. Shimoura, and Rodrigo F. O. Pena, University of Sao Paulo, Brazil 2015 SIAM Conference on Applications of Dynamical Systems 55

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS75 MS76 MS77 Between Order and Chaos: Networks of Chemical Recent Applications of Entropy and Information Oscillators Singular Perturbation Theory Processing in Complex 4:00 PM-6:00 PM - Part II of II Dynamics Room:Primrose A 4:00 PM-6:00 PM 4:00 PM-6:00 PM Chemical oscillations, which are a Room:Primrose B Room:Superior B remarkable nonequilibrium phenomenon, For Part 1 see MS70 can be observed in chemical engineering Complex systems often exhibit a fine balance Singularly perturbed dynamical systems arise applications and are ubiquitous in biological in many applications; for example, whenever between order and chaos. On one hand, high- systems. The realization of networks of dimensional deterministic dynamical systems there is a natural separation of time scales coupled chemical oscillators with control or a bifurcation that changes the underlying can show sensitive dependence on initial over the coupling function and topology is conditions wile on the other, identifying structure of a system. Many techniques a challenging experimental task, even for have been developed to study such systems. sensible macroscopic physical observables small and intermediate network sizes. In this relies on emergent coherent coarse-grained Geometric singular perturbation methods use workshop we report on recent experiments in properties of “geometric” dynamical objects structures. The recent years have seen which the coupling between the oscillatory the application of information-theoretic such as invariant manifolds and foliations. chemical reactions is realized via microfluid On the other hand, spectral techniques have aspects to a variety of complex dynamics, arrays, optical feedback or wired connections ranging from stochastic thermodynamics to been used to study transitions between in electrochemical arrays. The experiments linear operators that are posed on different neuroscience. In this symposium, we review demonstrate the connection between the some of these aspects and discuss relations spaces but are nevertheless “close’’. This rich dynamical behavior and the network minisymposium presents recent theoretical between notions of entropy and information topology. arising in various dynamical descriptions results for which singular perturbation theory used in complexity science. Organizer: Ralf Toenjes plays a key role in the analysis. Potsdam University, Germany Organizer: Bernhard Altaner Organizer: Kelly Mcquighan Max Planck Institute for Dynamics and 4:00-4:25 Synchronization and Boston University, USA Self-Organization, Germany Network Topology of Electrochemical Organizer: Hermen Jan Hupkes Micro-Oscillators in On-Chip University of Leiden, The Netherlands Organizer: Guillaume Lajoie Integrated Flow Cells University of Washington, USA Istvan Z. Kiss, Yanxin Jia, Yifan Liu, and Organizer: Peter van Heijster 4:00-4:25 Entropy, Dissipation and Jasmine Coleman, Saint Louis University, Queensland University of Technology, Information Processing in Models of USA Australia Complex Systems 4:30-4:55 Microfluidic Networks of 4:00-4:25 Pinning and Unpinning in Bernhard Altaner, Max Planck Institute Belousov-Zhabotinsky Drops Nonlocal Equations for Dynamics and Self-Organization, Seth Fraden, Brandeis University, USA Taylor Anderson, Mount Holyoke College, Germany USA; Gregory Faye, École des Hautes 5:00-5:25 Synchronization in Networks Etudes en Sciences Sociales, France; 4:30-4:55 Deconstructing Maxwell’s of Coupled Chemical Oscillators Arnd Scheel, University of Minnesota, Demon Kenneth Showalter, West Virginia Minneapolis, USA; David Stauffer, Dibyendu Mandal, University of University, USA California, Berkeley, USA Cornell University, USA 5:30-5:55 Long Transients to 4:30-4:55 Singularities in Front 5:00-5:25 Degrees of Information Synchronization in Random Networks Bifurcations with Scale Separation Processing in Chaotic Dynamical of Electrochemical Oscillators Jens Rademacher, University of Bremen, Systems Ralf Toenjes, Potsdam University, Germany Ryan G. James, University of California, Germany; Michael Sebek and Istvan Z. Davis, USA Kiss, Saint Louis University, USA 5:00-5:25 Travelling Waves and 5:30-5:55 Time-Dependent Chaotic Canards in a Model of Wound Attractors Shape Information Content Healing Angiogenesis in Neural Networks Kristen Harley and Peter van Heijster, Guillaume Lajoie, University of Queensland University of Technology, Washington, USA Australia; Robert Marangell, University of Sydney, Australia; Graeme Pettet, Queensland University of Technology, Australia; Martin Wechselberger, University of Sydney, Australia 5:30-5:55 Canard Supersonique Martin Wechselberger, University of Sydney, Australia 56 2015 SIAM Conference on Applications of Dynamical Systems

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 MS97 CP26 CP27 Dynamical Models in Drug Topics in Financial Topics in Biological Delivery Dynamical Systems and Dynamics IV 4:00 PM-6:00 PM Related Themes 4:00 PM-6:00 PM Room:Ballroom III 4:00 PM-5:00 PM Room:Magpie B Mathematical modeling of drug delivery Room:Magpie A Chair: Linda Sommerlade, University of has been attracting great attention of Aberdeen, United Kingdom Chair: To Be Determined scientists for years. It provides an adequate 4:00-4:15 Analysis of Cholera 4:00-4:15 Constant Rebalanced quantitative description of physical, chemical Epidemics with Bacterial Growth and Portfolio Strategy Is Rational in a and biological processes that determine the Spatial Movement performance of drug delivery systems. The Multi-Group Asset Trading Model Xueying Wang, Washington State goal of this minisymposium is to present Mark DeSantis, Chapman University, USA; University, USA recent advances in modeling basic types David Swigon, University of Pittsburgh, of drug delivery, including systems based USA 4:20-4:35 Optogenetic Stimulation of a Meso-Scale Human Cortical Model on fluid flows, swelling and deswelling 4:20-4:35 How Monetary Policy Can gels, liquid films, nanoparticles and lipid Cause Forecasting Uncertainty Prashanth Selvaraj and Andrew J. Szeri, University of California, Berkeley, USA; membranes, as well as transdermal drug James M. Haley, Point Park University, James W. Sleigh, University of Auckland, delivery systems. USA New Zealand; Heidi E. Kirsch, University Organizer: Alexander 4:40-4:55 Non-Smooth Dynamics and of California, San Francisco, USA Nepomnyashchy Bifurcations in a Model of Electricity Technion - Israel Institute of Market 4:40-4:55 Growth Dynamics for Pomacea Maculata Technology, Israel Gerard Olivar Tost and Johnny Valencia and Karyn L. Sutton, Calvo, Universidad Nacional de Colombia, Lihong Zhao Organizer: Vladimir Volper University of Louisiana, Lafayette, USA; Colombia Northwestern University, USA Jacoby Carter, USGS National Wetlands 4:00-4:25 Cyclic Drug Delivery Research Center, USA Devices and Monotone Dynamical 5:00-5:15 Assessing the Strength of Systems Directed Influences Among Neural Maria-Carme Calderer, University of Signals Minnesota, USA Linda Sommerlade and Marco Thiel, 4:30-4:55 Evaluation of the Diffusion University of Aberdeen, United Kingdom; Coefficient of Nanoparticles Using Claude Wischik, TauRx Therapeutics Ltd., Mathematical Simulation Singapore; Bjoern Schelter, University of Giora Enden and Amnon Sintov, Ben- Aberdeen, United Kingdom Gurion University of the Negev, Israel 5:20-5:35 Benefits of Noise in Synaptic 5:00-5:25 Fluid Flow and Drug Delivery Vesicle Release in a Brain Tumor Calvin Zhang and Charles S. Peskin, Ranadhir Roy and Daniel Riahi, University Courant Institute of Mathematical of Texas - Pan American, USA Sciences, New York University, USA 5:30-5:55 Viscoelastic Effects in Drug 5:40-5:55 Towards Understanding Delivery Mechanisms of Pain Transmission: a Alexander Nepomnyashchy, Technion Systems Theoretic Approach - Israel Institute of Technology, Israel; Pierre Sacré and Sridevi Sarma, Johns Vladimir A. Volpert, Northwestern Hopkins University, USA University, USA; Yulia Kanevsky, Technion - Israel Institute of Technology, Israel 2015 SIAM Conference on Applications of Dynamical Systems 57

Tuesday, May 19 Tuesday, May 19 Tuesday, May 19 CP28 CP29 PP1 Topics in Feedback/Control/ Topics in Pattern Formation II Poster Session and Dessert Optimization II 4:00 PM-5:20 PM Reception 4:00 PM-5:00 PM Room:Wasatch B 8:30 PM-10:30 PM Room:Wasatch A Chair: Víctor Brena-Medina, University Room:Ballroom Chair: Raya Horesh, IBM T.J. Watson of Bristol, United Kingdom The Breakup of Invariant Tori in 4-D Research Center, USA 4:00-4:15 Symmetry Groups and Maps Using the Slater’s Criterion Celso Abud and Ibere L. Caldas, University 4:00-4:15 Towards a Structural Theory Dynamics of Time-Fractional Diffusion of Sao Paulo, Brazil of Controllability of Binary Networks Equation Afroza Shirin, University of New Mexico, Muhammad D. Khan, Institute of Business Theta Model for Quartic Integrate- USA Management, Pakistan and-Fire Neuron Model Akihiko Akao and Yutaro Ogawa, University 4:20-4:35 Optimal Treatment Strategies 4:20-4:35 Polynomial Mixing Rates of of Tokyo, Japan; Bard Ermentrout, for HIV-TB Co-Infected Individuals Particle Systems University of Pittsburgh, USA; Yasuhiko Abhishek Mallela, University of Missouri, Yao Li, Courant Institute of Mathematical Jimbo and Kiyoshi Kotani, University of Kansas City, USA; Suzanne M. Lenhart, Sciences, New York University, USA Tokyo, Japan University of Tennessee, USA; Naveen K. 4:40-4:55 Stripe to Spot Transition in a Vaidya, University of Missouri, Kansas Plant Root Hair Initiation Model A Solution of Linear Programming City, USA Victor F. Brena-Medina, University Problems with Interval Coefficients Ibraheem Alolyan, King Saud University, 4:40-4:55 Optimal Control of Building’s of Bristol, United Kingdom; Daniele Saudia Arabia Hvac System with on-Site Energy Avitabile, University of Nottingham, Storage and Generation System United Kingdom; Alan R. Champneys, Developing a Model Approximation Raya Horesh, Young M. Lee, and Leo University of Bristol, United Kingdom; Method and Parameter Estimates for a Liberti, IBM T.J. Watson Research Michael Ward, University of British Solar Thermochemistry Application Center, USA; Young Tae Chae, Hyundai Columbia, Canada William D. Arloff, Karl Schmitt, Luke Engineering & Construction Co., Ltd, 5:00-5:15 Onset of Singularities in the Venstrom, and Leandro Jaime, Valparaiso Korea; Rui Zhang, IBM T.J. Watson Pattern of Fluctuational Paths of a University, USA Research Center, USA Nonequilibrium System Hamiltonian Hopf Bifurcations in Oleg B. Kogan, Cornell University, Schrödinger Trimers USA; Mark I. Dykman, Michigan State Casayndra H. Basarab and Roy Goodman, University, USA New Jersey Institute of Technology, USA Computing the Optimal Path in Stochastic Dynamical Systems Dinner Break Martha Bauver, Lora Billings, and Eric Forgoston, Montclair State University, USA 6:00 PM-8:30 PM Effects of Quasi-Steady-State Attendees on their own Reduction on Biophysical Models with Oscillations Sebastian D. Boie, Vivien Kirk, and James SIADS Editorial Sneyd, University of Auckland, New Zealand Board Meeting Analyzing Cycling Dynamics in 6:30 PM-8:30 PM Stochastic Systems Room: Summit Room Pralhad Burli, Lora Billings, and Eric Forgoston, Montclair State University, USA Limit Cycles in a Simplified Basal Ganglia Model Michael Caiola and Mark Holmes, Rensselaer Polytechnic Institute, USA

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Tuesday, May 19 Spike Adding in Transient Dynamics Discriminating Chaotic and Stochastic Saeed Farjami, Hinke M. Osinga, and Dynamics Through the Permutation PP1 Vivien Kirk, University of Auckland, New Spectrum Test Zealand Christopher W. Kulp, Lycoming College, Poster Session and Dessert USA; Luciano Zunino, Centro de Front-Dynamics and Pattern Selection Investigaciones en Optica, Mexico Reception in the Wake of Triggered Instabilities 8:30 PM-10:30 PM Ryan Goh and Arnd Scheel, University of Coupling Methods As a Tool for Minnesota, USA Sensitivity Analysis of Stochastic Room:Ballroom Differential Equations Pattern Sequences as Early-warning Andrew Leach, University of Arizona, USA cont. Signs of Critical Transition in Models of Dryland Vegetation Transient Dynamics in Ensemble of Karna V. Gowda, Yuxin Chen, Sarah Iams, Inhibitory Coupled Rulkov Maps Mathematical Modelling of Spatial and Mary Silber, Northwestern University, Tatiana A. Levanova and Grigory Osipov, Sorting and Evolution in a Host- USA Lobachevsky State University of Nizhny Novgorod, Russia Parasite System Rigorous Computation of Radially Matthew H. Chan, Gregory Brown, Symmetric Stationary Solutions of Complex Collective Behavior in Richard Shine, and Peter S. Kim, Pdes a Network of Theta Neurons is University of Sydney, Australia Chris M. Groothedde, VU University, Suppressed by Synaptic Diversity New Computational Tools for Non- Amsterdam, Netherlands Lucas Lin, Thomas Jefferson High School of Science and Techonology, USA; Paul Smooth Dynamical Systems Dynamics of Register Transitions in So and Ernest Barreto, George Mason Antonio S. Chong and Marian Wiercigroch, Human Vocal Fold Modeling University, USA University of Aberdeen, United Kingdom Jesse Haas, Grenoble University, France Shape Coherence and Finite- Polyrhythmic Synchronization in A Mathematical Model of Saliva Time Curvature Evolution in Time- Modular Networks Secretion and Calcium Dynamics Dependent Dynamical Systems Jarod Collens, Justus T. Schwabedal, Andrey Jung Min Han, James Sneyd, and Vivien Tian Ma and Erik Bollt, Clarkson University, Shilnikov, and Drake Knapper, Georgia Kirk, University of Auckland, New USA State University, USA Zealand Snaking on Networks: From Local Modeling the Lymphocytic Mixed-Mode Oscillations and Twin Solutions to Turing Patterns Choriomeningitis Virus: Insights into Canards Nick McCullen, University of Bath, Understanding Its Epidemiology in the Ragheb Hasan, Hinke M. Osinga, and United Kingdom; Matthias Wolfrum, Wild Bernd Krauskopf, University of Auckland, Weierstrass Institute for Applied Analysis Christy Contreras, Arizona State New Zealand University, USA and Stochastics, Germany; Thomas A Dynamical Analysis of Steam Wagenknecht, University of Leeds, United Causal Relationships Between Time Supply Network Based on Invariant Kingdom Series: Generalizing Takens’ Theorem Manifold Fractal Boundaries in the Parameters to a Dynamical Network Hikaru Hoshino and Yoshihiko Susuki, Space of Deterministic Dynamical Bree Cummins and Tomas Gedeon, Kyoto University, Japan Montana State University, USA; Kelly Systems Spendlove, Rutgers University, USA Defects in Spatially Extended Systems Everton S. Medeiros, University of Gabriela Jaramillo, University of Sao Paulo, Brazil; Iberê L. Caldas, Regular Acceleration from Low Initial Minnesota, USA; Arnd Scheel, University Universidade de Sao Paulo, Brazil; Murilo Energies in a Magnetized Relativistic of Minnesota, Minneapolis, USA Baptista, University of Aberdeen, United System Kingdom Meirielen C. De Sousa and Iberê L. Delayed Feedback Model of Axonal Caldas, Universidade de Sao Paulo, Brazil; Length Sensing A Biophysical Model for the Role of Fernanda Steffens, Deutsches Elektronen- Bhargav R. Karamched, University of Network Topology in Regulating a Synchrotron, Germany; Renato Pakter and Utah, USA; Paul C. Bressloff, University Two-Phase Breathing Rhythm Felipe Rizzato, Universidade Federal do of Utah, USA and University of Oxford, Joshua Mendoza, Kameron Decker Rio Grande do Sul, Brazil United Kingdom Harris, and Eric Shea-Brown, University of Washington, USA; Jan Ramirez and ∞ Nonlinear Dynamical Systems in Estimating the L -Norm of Linear Tatiana Dashevskiy, Seattle Children’s Finance Solutions of Cahn-Hilliard Research Institute, USA Philipp Düren, Universität Augsburg, Deniz K. Kiliç, Middle East Technical Modeling Effects of Drugs of Abuse on Germany University, Turkey Hiv-Specific Antibody Responses Jones M. Mutua, Anil Kumar, and Naveen K. Vaidya, University of Missouri, Kansas City, USA

continued in next column continued on next page 2015 SIAM Conference on Applications of Dynamical Systems 59

Time-Delayed Model of Immune Robust Pulse Generators in An Response in Plants Excitable Medium Wednesday, Giannis Neofytou and Konstantin Blyuss, Takashi Teramoto, Asahikawa Medical University of Sussex, United Kingdom University, Japan May 20 Analysis and Control of Pre-Extinction Dynamical Building Blocks in Dynamics in Stochastic Populations Turbulent Two-Dimensional Channel Garrett Nieddu, Lora Billings, and Eric Flow Registration Forgoston, Montclair State University, Toshiki Teramura and Sadayoshi Toh, 8:00 AM-4:30 PM USA Kyoto University, Japan Room:Ballroom Foyer An Explicit Formula for R0 of Tick- Phase Models and Oscillators with Borne Relapsing Fever Time Delayed All-to-All Coupling Cody Palmer, University of Montana, USA Zhen Wang, University of Waterloo, Canada MS78 Title Not Available Youngmin Park, University of Pittsburgh, Efficient Design of Navigable Dynamics of Moreau USA Networks Sweeping Processes - B.M. Shandeepa D. Wickramasinghe and Stochastic Motion of Bumps in Planar Part I of II Jie Sun, Clarkson University, USA Neural Fields Daniel Poll and Zachary Kilpatrick, Instability of Certain Equilibrium 8:30 AM-10:30 AM University of Houston, USA Solutions of the Euler Fluid Equations Room:Ballroom I Joachim Worthington, Holger R. Dullin, Automatically Proving Periodic For Part 2 see MS91 and Robby Marangell, University of Solutions to Polynomial ODEs A sweeping process describes the motion of Sydney, Australia Elena Queirolo, Vrije Universiteit a particle which is governed by a differential Amsterdam, The Netherlands A Symbolic Method in Chua’s Circuit equation on the one hand and which is Tingli Xing and Andrey Shilnikov, Georgia constrained by a moving convex set on the Repulsive Inhibition Promotes State University, USA other hand. Such a configuration leads to a Synchrony in Excitatory Networks of differential inclusion with unbounded right- Bursting Neurons Interactions of Solitary Modes in hand-terms (Clarke normal cones). Building Reimbay Reimbayev and Igor Belykh, Models of Bacterial Chemotaxis upon the discrete approximation scheme Georgia State University, USA Glenn S. Young, Hanna Salman, Bard proposed my Moreau in 70th the theory of Ermentrout, and Jonathan Rubin, Quasipatterns in Two and Three sweeping processes is now able to analyse the University of Pittsburgh, USA Dimensions existence, continuous dependence, periodicity Alastair M. Rucklidge, University of The Spread of Activity with Refractory and (Lyapunov) stability of solutions. Leeds, United Kingdom Periods over Directed Networks This minisymposium accumulates current and Alla Borisyuk, achievements aiming to approach the structural Rigorous Computations for BVPs with Daniel R. Zavitz stability and to understand how the dynamics Chebyshev-series University of Utah, USA changes under varying parameters (control). Ray Sheombarsing, VU University, Using Tangles to Quantify Topological Amsterdam, Netherlands Mixing of Fluids Organizer: Oleg Makarenkov , Sulimon Sattari, and Kevin Central Configurations of Qianting Chen University of Texas at Dallas, USA Symmetrically Restricted Five-Body A. Mitchell, University of California, 8:30-8:55 On the Response of Sweeping Problem Merced, USA Processes to Perturbation Anoop Sivasankaran, Khalifa University Computing Chaotic Transport Mikhail Kamenski, Voronezh State University, of Science, Technology and Research, Properties in a Mixed Phase Space Russia; Oleg Makarenkov, University of United Arab Emirates; Muhammad Shoaib with Periodic Orbits Texas at Dallas, USA and Abdulrehman Kashif, University of Sulimon Sattari and Kevin A. Mitchell, 9:00-9:25 Dynamics of Sweeping Hail, Saudi Arabia University of California, Merced, USA Processes with Jumps in the Driving Finite Time Diagnostics and Transport Term Barriers in Non Twist Systems Vincenzo Recupero, Politecnico di Torino, Jose D. Szezech Jr, Ponta Grossa State Italy University, Brazil; Ibere L. Caldas, 9:30-9:55 Control of Moreau’s Sweeping University of Sao Paulo, Brazil; Sergio Process: Some Results and Open R. Lopes and Ricardo L. Viana, Federal Problems University of Paraná, Brazil; Philip Giovanni Colombo, University of Padova, Morrison, University of Texas at Austin, Italy USA 10:00-10:25 Estimation and Control Problems in Systems with Moreau’s Sweeping Process Aneel Tanwani, University of Kaiserslautern, continued in next column Germany 60 2015 SIAM Conference on Applications of Dynamical Systems

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS79 MS80 MS81 Topological Fluid and Mass Theoretical Aspects of Spiral First Passage Times in Dynamics - Part I of II and Scroll Wave Dynamics - Discrete and Continuous 8:30 AM-10:30 AM Part I of II Systems - Part I of II Room:Ballroom II 8:30 AM-10:30 AM 8:30 AM-10:30 AM For Part 2 see MS92 Room:Ballroom III Room:Magpie A Topological and geometrical methods For Part 2 see MS93 For Part 2 see MS94 provide powerful tools for predicting and Spiral and scroll waves are the most common Numerous problems in nature are formulated interpreting the dynamics of fluid flows and types of solutions characterizing the dynamics in terms of Mean First Passage Time (MFPT) interacting masses. This minisymposium of 2- and 3-dimensional excitable media such of Brownian particles in the presence of traps. will explore recent developments in the use as the cardiac tissue. This minisymposium For example, cells are regulated by chemical of these methods for considering relative presents a sampling of recent analytical and reactions involving signaling molecules that equilibria, modeling interaction dynamics numerical studies focusing on the interaction have to find their targets in a complex and on surfaces, and characterizing structure of scroll and spiral waves with perturbations crowded environment. The study of MFPT and transport in complex flows. This such as structural heterogeneities and external touches upon many topics and utilizes diverse minisymposium is dedicated to Konrad Bajer stimuli as well as self-interactions and tools including PDEs, stochastic differential (1956-2014), who made many contributions interaction of different spiral/scroll waves with equations, complex variables, generating in this area. each other. functions and many others. This mini-session Organizer: Stefanella Boatto Organizer: Roman Grigoriev will bring together experts in this active field of research. Directions that will be considered Universidade Federal do Rio De Georgia Institute of Technology, USA Janeiro, Brazil include: search-and-rescue, mobile traps, Organizer: Vadim N. Biktashev narrow escape problems on bounded domains, Organizer: Mark A. Stremler University of Exeter, United Kingdom connections to spike solutions of PDEs, and Virginia Tech, USA 8:30-8:55 Drift of Scroll Waves in Thin applications in biology and physics. 8:30-8:55 Eulerian Geometric Layers Caused by Thickness Features Organizer: Alan E. Lindsay Integration of Fluids for Computer Irina Biktasheva, University of Liverpool, University of Notre Dame, USA Graphics United Kingdom; Hans Dierckx, Ghent Mathieu Desbrun, California Institute University, Belgium; Vadim N. Biktashev, Organizer: Justin C. Tzou of Technology, USA; Dmitry Pavlov, University of Exeter, United Kingdom Dalhousie University, Canada Imperial College London, United 9:00-9:25 Spiral Pinballs 8:30-8:55 First Passage Times in Kingdom; Evan S. Gawlik, Stanford Jacob Langham and Dwight Barkley, Biological Self-Assembly University, USA; Yiying Tong, Michigan University of Warwick, United Kingdom Maria D’Orsogna, California State State University, USA; Gemma Mason, University, Northridge, USA; Tom Chou, California Institute of Technology, USA; 9:30-9:55 Tidal Forces Act on Cardiac University of California, Los Angeles, USA Eva Kanso, University of Southern Filaments 9:00-9:25 Asymptotic Analysis of California, USA Hans Dierckx, Ghent University, Belgium Narrow Escape Problems in Non- 9:00-9:25 Poincare-Birkhoff Normal 10:00-10:25 Computation of Unstable Spherical 3D Domains Forms for Hamiltonian Relative Solutions of Cardiac Models on Static Alexei F. Cheviakov, University of Equilibria and Evolving Domains Saskatchewan, Canada; Daniel Gomez, Cristina Stoica, Wilfrid Laurier University, Christopher Marcotte and Roman Grigoriev, University of British Columbia, Canada Canada Georgia Institute of Technology, USA 9:30-9:55 Signal Focusing Through 9:30-9:55 The Dynamics of Vortices Active Transport and Masses over Surfaces of Aljaz Godec and Ralf Metzler, Universität Revolution Potsdam, Germany Stefanella Boatto and Gladston Duarte, 10:00-10:25 First-Passage Times Universidade Federal de Rio de Janeiro, of Random Walks in Confined Brazil; David G. Dritschel, University of Geometries St. Andrews, United Kingdom; Teresa J. Stuchi, Universidade Federal de Rio de Olivier Benichou, Université Pierre et Marie Janeiro, Brazil; Carles Simo, Universitat Curie, France de Barcelona, Spain; Rodrigo Schaefer, Universitat Politecnica de Catalunya, Spain 10:00-10:25 Studies on Dynamics of Vortices on a Flat Torus Humberto H. de Barros Viglioni, Universidade Federal de Sergipe, Brazil 2015 SIAM Conference on Applications of Dynamical Systems 61

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS82 MS83 MS84 Control of Multiscale Wave Propagation in Highly Dynamics of Neural Dynamics - Part I of II Nonlinear Dispersive Media Networks with General 8:30 AM-10:30 AM - Part I of II Connectivity and Room:Magpie B 8:30 AM-10:30 AM Nonlinearity For Part 2 see MS95 Room:Wasatch A 8:30 AM-10:30 AM The control of dynamical systems has been For Part 2 see MS96 Room:Wasatch B extensively studied in the past century, Wave propagation in highly nonlinear The dynamics of a neural field model can which led to significant applications such dispersive media has recently attracted as space mission, aerocraft design, or be analyzed using a nonlinear integro- considerable attention of the interdisciplinary differential equation. Two basic components nanoelectromechanical systems. Multiscale community that includes applied simulation and modeling, on the other in this model are the integral kernel, which mathematicians, physicists and engineers. models the network connectivity, and the hand, has become an active field in recent In particular, dynamics of granular crystals years, due to the multiscale nature of nonlinear gain function. Many previous has been a subject of intensive theoretical results are obtained under rather restrictive complex systems ubiquitous in practical and experimental research because of their applications. We consider it an emerging assumptions on the connectivity and the unique, adaptive dynamical properties. gain. In this minisymposium, we will direction to go further and control multiscale Strongly nonlinear dispersive media may systems, which was not possible without present some recent theoretical as well as exhibit quite intriguing phenomena such experimental works for more general types contemporary multiscale methods and as broadband absorption, high-rate wave computational architectures. The proposed of connectivity functions and gain functions. attenuation and strong energy localization, The talks will discuss analytical tools for and minisymposium gathers researchers working rendering them highly attractive for on frontiers of related fields, with goals of dynamical consequences of generalizations multiple engineering applications. In this such as anisotropy/inhomogeneity in the shaping this new direction and contributing minisymposium, leading experts dealing with to important applications. connectivity functions and non-monotonicity this class of dynamical systems will come in the gain functions. Organizer: Molei Tao together for a creative exchange of ideas Georgia Institute of Technology, USA involving fundamental and applied research. Organizer: Dennis Yang Drexel University, USA 8:30-8:55 Control of Multiscale Organizer: Anna Vainchtein Dynamical Systems University of Pittsburgh, USA 8:30-8:55 Asymmetric Stationary Bumps in Neural Field Models Richard D. Braatz, Massachusetts Institute Organizer: Yuli Starosvetsky Dennis Yang, Drexel University, USA of Technology, USA Technion - Israel Institute of Technology, 9:00-9:25 Some Results on the Israel 9:00-9:25 Homogenization Theory for Backward Stability of Singular Neural Field Models 8:30-8:55 Granular Acoustic Switches Perturbation Approximations of Linear John Wyller, Norwegian University of Life and Logic Elements and Nonlinear Stochastic Control Sciences, Norway Jinkyu Yang and Feng Li, University of Systems Washington, USA; Paul Anzel, California 9:30-9:55 Traveling Patterns in Lateral Carsten Hartmann, Free University Inhibition Neural Networks Institute of Technology, USA; Panayotis Amsterdam, Netherlands Kevrekidis, University of Massachusetts, Yixin Guo and Aijun Zhang, Drexel 9:30-9:55 Variational Integrators for USA; Chiara Daraio, ETH Zürich, University, USA Multiscale Dynamics Switzerland and California Institute of 10:00-10:25 Modulating Synaptic Sina Ober-Bloebaum, University of Technology, USA Plasticity Within In Vitro Hippocampal Paderborn, Germany; Sigrid Leyendecker, 9:00-9:25 Nonlinear Waves in Networks University of Erlangen-Nuremberg, Microsphere-Based Metamaterials Rhonda Dzakpasu, Georgetown University, Germany Nicholas Boechler, University of USA 10:00-10:25 Control of Oscillators, Washington, USA Temporal Homogenization, and 9:30-9:55 Multiscale Analysis of Energy Harvest by Super-Parametric Strongly Localized Waves Resonance Guillaume James, Université de Grenoble Molei Tao, Georgia Institute of Technology, and CNRS, France USA 10:00-10:25 Standing Waves on Tadpole Graphs Dmitry Pelinovsky, McMaster University, Canada 62 2015 SIAM Conference on Applications of Dynamical Systems

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS85 MS86 MS87 Advances in Viral Infection Front Propagation in Nonsmooth Dynamical Modeling - Part I of II Advection-Reaction- Systems: Theory and 8:30 AM-10:30 AM Diffusion Systems - Applications - Part I of II Part I of II Room:Maybird 8:30 AM-10:30 AM For Part 2 see MS98 8:30 AM-10:30 AM Room:Superior B Viral infections, be they acute, like Room:Superior A For Part 2 see MS100 influenza or ebola, or chronic, like HIV, For Part 2 see MS99 Many physical systems involve abrupt events, pose a continuing threat to daily life. In Autocatalytic reactions in a spatially-extended such as switches, impacts or thresholds, recent years mathematical modeling has system are characterized by the propagation and are well-modelled by equations that are become an important tool in investigating of reaction fronts separating the species. The nonsmooth. This minisymposium will discuss these infections, and novel methods are front dynamics is generally well-understood novel applications of nonsmooth systems in rapidly emerging. The primary goal of this for reaction-diffusion systems in the absence ecology, optics and neuroscience, as well as minisymposium is to provide a platform for of substrate flow. The effects of fluid motion describe new developments in the theory of discussion of mathematical advances in viral on fronts in the general advection-reaction- nonsmooth systems. Overall the talks will infection modeling and resulting insights into diffusion (ARD) case have only recently highlight the various nuances of nonsmooth viral infections, at both the within-host and received significant attention, despite the wide systems and show how these relate to the between-hosts (epidemiological) scales. applicability of ARD, including microfluidic dynamical behaviour of the physical systems Organizer: Jessica M. Conway chemical reactors, plasmas, ecosystem being modelled. Pennsylvania State University, USA dynamics in the oceans (e.g., plankton Organizer: David J. Simpson Organizer: Naveen K. Vaidya blooms), cellular- and embryonic-scale Massey University, New Zealand biological processes. This minisymposium University of Missouri, Kansas City, USA 8:30-8:55 Infinitely Many Coexisting brings together groups studying ARD systems Attractors in the Border-Collision 8:30-8:55 A Multi-Scale Model of from a variety of perspectives, including Normal Form Multiple Exposures to a Pathogen experiments, dynamical systems theory, David J. Simpson, Massey University, New Jane Heffernan and Redouane Qesmi, York numerical PDEs, and analytics. University, Canada; Jianhong Wu, York Zealand Organizer: Kevin A. Mitchell University, Canada 9:00-9:25 Geometric Optics and University of California, Merced, USA 9:00-9:25 Contact Network Models for Piecewise Linear Systems Immunizing Infections Organizer: Thomas H. Solomon Paul Glendinning, University of Shweta Bansal, Georgetown University, Bucknell University, USA Manchester, United Kingdom USA Organizer: John R. Mahoney 9:30-9:55 Analysis of Traveling Pulses 9:30-9:55 Evaluation of Combined University of California, Merced, USA and Fronts in a Nonsmooth Neural Mass Model Strategies for Controlling Dengue 8:30-8:55 Front Pinning in Single Vortex Fever Flows Jeremy D. Harris, University of Pittsburgh, USA Alun Lloyd, North Carolina State University, John R. Mahoney and Kevin A. Mitchell, USA University of California, Merced, USA 10:00-10:25 Are Plankton Discontinuous, Smooth Or Slow-Fast 10:00-10:25 Mathematical Models of 9:00-9:25 Front Propagation in Cellular (and Furious)? the Spatial and Evolutionary Dynamics Flows for Fast Reaction and Small of Influenza A Diffusivity Sofia Piltz, University of Oxford, United Kingdom Julia R. Gog, University of Cambridge, Alexandra Tzella, University of Birmingham, United Kingdom United Kingdom; Jacques Vanneste, University of Edinburgh, United Kingdom 9:30-9:55 Experimental Studies of Burning Invariant Manifolds as Barriers to Reaction Fronts Savannah Gowen, Mount Holyoke College, USA; Tom Solomon, Bucknell University, USA 10:00-10:25 Propagation of An Autocatalytic Reaction Front in Heterogeneous Porous Media Laurent Talon, Université Paris-Sud, France; Dominique Salin, University of Pittsburgh School of Medicine, USA 2015 SIAM Conference on Applications of Dynamical Systems 63

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS88 MS89 MS90 Emergent Phenomena from Complex Network Theory Sensitivity Methods with Many-player Dynamics Based Approaches in Applications in Biological and Social the Analyses of Complex 8:30 AM-10:30 AM Systems Systems and Data - Room:Primrose B 8:30 AM-10:30 AM Part I of II Sensitivity and uncertainty analysis are Room:White Pine 8:30 AM-10:30 AM used to understand the role of variability inherent in the physical experimentation, Systems wherein the behavior of individual Room:Primrose A mathematical interpretation and organisms is controlled by simple interaction For Part 2 see MS102 mathematical analysis. We are interested rules, such as from discrete games, can lead Analysis of network data obtained from a in biological applications where to organized large scale dynamics. The global complex system is often a challenging task. uncertainty arises in each aspect of behavior can depend heavily on small nuances In this minisymposium we will be discussing the joint experimental and theoretical in the underlying interaction rules, as well as few novel approaches for obtaining insights studies. For example, immune response the network and/or structure on which these into the structural and functional properties to bacterial challenge has stochastic organisms reside. In this minisymposium, of empirical networks and networks inferred elements. Additionally all experiments have we will explore the dynamics that arise from from data. One of our focus areas will be to limited precision in measuring the data, various biological and social interactions employ simulation of variety of dynamical making parameter estimation challenging. within systems comprised of large numbers processes on networks to study properties Finally, model analysis typically requires of agents. of empirical networks. We will also discuss approximation such as perturbation or Organizer: Scott Mccalla methodologies to overcome problems in numerical methods. We focus on methods Montana State University, USA the analysis of empirical networks due to for quantifying uncertainty in biological spurious or missing links. Dynamical system processes, the sensitivity of the model with Organizer: Martin Short based approaches for transforming data respect to parameters and data assimilation Georgia Institute of Technology, USA into a network representing will also be methods. presented. 8:30-8:55 Hotspots in a Non-Local Organizer: Nick Cogan Crime Model Organizer: Nishant Malik Florida State University, USA Scott Mccalla, Montana State University, University of North Carolina at Chapel USA; Jonah Breslau, Pomona College, 8:30-8:55 Using Sensitivity Analysis to Hill, USA USA; Sorathan Chaturapruek, Harvey Understand S. aureus Infections Mudd College, USA; Theodore 8:30-8:55 Role of Netwok Topology in Angela M. Jarrett, Nick Cogan, and M Kolokolnikov, Dalhousie University, Collective Opinion Formation Yousuff Hussaini, Florida State University, Canada; Daniel Yazdi, University of Nishant Malik, University of North USA Carolina at Chapel Hill, USA California, Los Angeles, USA 9:00-9:25 Computational Aspects of 9:00-9:25 Co-Dimension One Self 9:00-9:25 Network Reliability As a Tool Stochastic Collocation with Multi- Assembly for Using Dynamics to Probe Network Fidelity Models James von Brecht, California State Structure Xueyu Zhu and Dongbin Xiu, University of University, Long Beach, USA; Scott Stephen Eubank, Yasamin Khorramzadeh, Utah, USA Mina Youssef, Shahir Mowlaei, and Mccalla, Montana State University, USA; 9:30-9:55 The Dynamics of Alopecia David T. Uminsky, University of San Madhurima Nath, Virginia Tech, USA Areata Francisco, USA 9:30-9:55 Linear Dynamics on Brain Atanaska Dobreva, Florida State 9:30-9:55 Swarming of Self-propelled Networks: A Tool for Understanding University, USA; Ralf Paus, University Particles in Fluids Cognition of Manchester, United Kingdom and Yaoli Chuang and Maria D’Orsogna, Danielle Bassett, University of Pennsylvania, University of Münster, Germany; Nicholas California State University, Northridge, USA and Fabio Pasqualetti, University of Cogan, Florida State University, USA California, Riverside, USA USA 10:00-10:25 Epistemic Uncertainty 10:00-10:25 Origin and Structure of 10:00-10:25 Dynamical Macro- Quantification Using Fuzzy Set Theory Dynamic Social Networks Based on Prudential Stress Testing Using YanYan He and Dongbin Xiu, University of Cooperative Actions Network Theory Utah, USA Christoph Hauert and Lucas Wardil, Dror Y. Kenett, Boston University, USA University of British Columbia, Canada Coffee Break 10:30 AM-11:00 AM Room:Golden Cliff 64 2015 SIAM Conference on Applications of Dynamical Systems

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 IP5 MS91 MS92 Cooperation, Cheating, Dynamics of Moreau Topological Fluid and Mass and Collapse in Biological Sweeping Processes - Dynamics - Part II of II Populations Part II of II 1:30 PM-3:30 PM 11:00 AM-11:45 AM 1:30 PM-3:30 PM Room:Ballroom II Room:Ballroom Room:Ballroom I For Part 1 see MS79 Topological and geometrical methods Chair: Jan Medlock, Oregon State For Part 1 see MS78 provide powerful tools for predicting and University, USA A sweeping process describes the motion of a particle which is governed by a differential interpreting the dynamics of fluid flows and Natural populations can suffer catastrophic equation on the one hand and which is interacting masses. This minisymposium collapse in response to small changes in constrained by a moving convex set on the will explore recent developments in the use environmental conditions as a result of a other hand. Such a configuration leads to a of these methods for considering relative bifurcation in the dynamics of the system. We differential inclusion with unbounded right- equilibria, modeling interaction dynamics have used laboratory microbial ecosystems to hand-terms (Clarke normal cones). Building on surfaces, and characterizing structure directly measure theoretically proposed early upon the discrete approximation scheme and transport in complex flows. This warning signals of impending population proposed my Moreau in 70th the theory of minisymposium is dedicated to Konrad Bajer collapse based on critical slowing down. Our sweeping processes is now able to analyse (1956-2014), who made many contributions experimental yeast populations cooperatively the existence, continuous dependence, in this area. break down sugar, meaning that below a periodicity and (Lyapunov) stability of Organizer: Stefanella Boatto critical size the population cannot sustain solutions. This minisymposium accumulates Universidade Federal do Rio De itself. The cooperative nature of yeast growth current achievements aiming to approach the Janeiro, Brazil on sucrose makes the population susceptible structural stability and to understand how the to “cheater” cells, which do not contribute to dynamics changes under varying parameters Organizer: Mark A. Stremler the public good and reduce the resilience of (control). Virginia Tech, USA the population. Organizer: Oleg Makarenkov 1:30-1:55 Braid Dynamics, Self- Jeff Gore University of Texas at Dallas, USA organized Criticality, and Solar Massachusetts Institute of Technology, Coronal Heating USA 1:30-1:55 Sweeping Process and Mitchell Berger, University of Exeter, Congestion Models for Crowd Motion United Kingdom Juliette Venel, Universite Lille-Nord de France, France 2:00-2:25 Topological Shocks in Burgers Turbulence 2:00-2:25 Evolution Equations Lunch Break Kostantin Khanin, University of Toronto, Governed by Sweeping Processes Canada 11:45 AM-1:30 PM and Applications in Heat Equations with Controlled Obstacles 2:30-2:55 Topology of Vortex Attendees on their own Hoang Nguyen, University of Technical Trajectories in Wake-Like Flows Federical Santa Maria, Chile Mark A. Stremler, Virginia Tech, USA 2:30-2:55 Periodic Solutions of 3:00-3:25 Characterizing Complexity Moreau Sweeping Processes and of Aperiodic Braids of Trajectories Applications Marko Budisic and Jean-Luc Thiffeault, Ivan Gudoshnikov, University of Texas at University of Wisconsin, Madison, USA Dallas, USA 3:00-3:25 Moreau Sweeping Processes on Banach Spaces Messaoud Bounkhel, King Saud University, Saudia Arabia 2015 SIAM Conference on Applications of Dynamical Systems 65

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS93 MS94 MS95 Theoretical Aspects of Spiral First Passage Times in Control of Multiscale and Scroll Wave Dynamics - Discrete and Continuous Dynamics - Part II of II Part II of II Systems - Part II of II 1:30 PM-3:30 PM 1:30 PM-3:30 PM 1:30 PM-3:30 PM Room:Magpie B Room:Ballroom III Room:Magpie A For Part 1 see MS82 For Part 1 see MS80 For Part 1 see MS81 The control of dynamical systems has been Spiral and scroll waves are the most Numerous problems in nature are formulated extensively studied in the past century, common types of solutions characterizing the in terms of Mean First Passage Time which led to significant applications such dynamics of 2- and 3-dimensional excitable (MFPT) of Brownian particles in the as space mission, aerocraft design, or media such as the cardiac tissue. This presence of traps. For example, cells are nanoelectromechanical systems. Multiscale minisymposium presents a sampling of recent regulated by chemical reactions involving simulation and modeling, on the other analytical and numerical studies focusing signaling molecules that have to find hand, has become an active field in recent on the interaction of scroll and spiral their targets in a complex and crowded years, due to the multiscale nature of waves with perturbations such as structural environment. The study of MFPT touches complex systems ubiquitous in practical heterogeneities and external stimuli as well as upon many topics and utilizes diverse tools applications. We consider it an emerging self-interactions and interaction of different including PDEs, stochastic differential direction to go further and control multiscale spiral/scroll waves with each other. equations, complex variables, generating systems, which was not possible without contemporary multiscale methods and Organizer: Roman Grigoriev functions and many others. This mini- session will bring together experts in this computational architectures. The proposed Georgia Institute of Technology, USA active field of research. Directions that will minisymposium gathers researchers working Organizer: Vadim N. Biktashev be considered include: search-and-rescue, on frontiers of related fields, with goals of University of Exeter, United Kingdom mobile traps, narrow escape problems on shaping this new direction and contributing to important applications. 1:30-1:55 Interaction of Electric Field bounded domains, connections to spike Stimuli with Scroll Waves in Three solutions of PDEs, and applications in Organizer: Molei Tao Dimensions biology and physics. Georgia Institute of Technology, USA Niels Otani, Rochester Institute of Organizer: Alan E. Lindsay 1:30-1:55 Control of a Model of DNA Technology, USA; Valentin Krinski, University of Notre Dame, USA Opening Dynamics via Resonance CNRS, France Organizer: Justin C. Tzou with a Terahertz Field Wang-Sang Koon, California Institute of 2:00-2:25 Unusually Simple Way to Dalhousie University, Canada Create Spiral Wave in An Excitable Technology, USA Medium 1:30-1:55 Uniform Asymptotic Approximation of Diffusion to a Small 2:00-2:25 A Dynamical Switching of Vladimir Zykov, Alexei Krekhov, and Target Reactive and Nonreactive Modes at Eberhard Bodenschatz, Max-Planck- High Energies Jay Newby, The Ohio State University, Institute for Dynamics and Self- USA Tamiki Komatsuzaki, Hokkaido University, Organization, Germany Japan; Mikito Toda, Nara Women’s 2:00-2:25 Narrow Escape to Traps with 2:30-2:55 Describing Scroll Wave Ring University, Japan; Hiroshi Teramoto, Absorbing and Reflecting Portions Interactions Via Interacting Potentials Hokkaido University, Japan Alan E. Lindsay, University of Notre Flavio M. Fenton, Georgia Institute of 2:30-2:55 Mode-Specific Effects Dame, USA Technology, USA; Jairo Rodriguez and in Structural Transitions of Atomic Daniel Olmos, Universidad de Sonora, 2:30-2:55 Sampling First-Passage Clusters with Multiple Channels Mexico Events When Drift Is Included in the Tomohiro Yanao, Waseda University, Japan First-Passage Kinetic Monte Carlo 3:00-3:25 On the Generation of Method 3:00-3:25 Obtaining Coarse-Grained Spiral and Scroll Waves by Periodic Models from Multiscale Data Ava Mauro, University of Notre Dame, Stimulation of Excitable Media in the Sebastian Krumscheid, École Presence of Obstacles of Minimum USA; Samuel A. Isaacson, Boston University, USA Polytechnique Fédérale de Lausanne, Size Switzerland; Greg Pavliotis and Serafim Daniel Olmos and Humberto Ocejo, 3:00-3:25 Drunken Robber, Tipsy Cop: Kalliadasis, Imperial College London, Universidad de Sonora, Mexico First Passage Times, Mobile Traps, and United Kingdom Hopf Bifurcations Justin C. Tzou, Shuangquan Xie, and Theodore Kolokolnikov, Dalhousie University, Canada 66 2015 SIAM Conference on Applications of Dynamical Systems

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS96 MS98 MS99 Wave Propagation in Highly Advances in Viral Infection Front Propagation in Nonlinear Dispersive Media Modeling - Part II of II Advection-Reaction- - Part II of II 1:30 PM-3:30 PM Diffusion Systems - 1:30 PM-3:30 PM Room:Maybird Part II of II Room:Wasatch A For Part 1 see MS85 1:30 PM-3:30 PM Viral infections, be they acute, like For Part 1 see MS83 Room:Superior A influenza or ebola, or chronic, like HIV, Wave propagation in highly nonlinear pose a continuing threat to daily life. In For Part 1 see MS86 dispersive media has recently attracted recent years mathematical modeling has Autocatalytic reactions in a spatially-extended considerable attention of the interdisciplinary become an important tool in investigating system are characterized by the propagation community that includes applied these infections, and novel methods are of reaction fronts separating the species. The mathematicians, physicists and engineers. rapidly emerging. The primary goal of this front dynamics is generally well-understood In particular, dynamics of granular crystals minisymposium is to provide a platform for for reaction-diffusion systems in the absence has been a subject of intensive theoretical discussion of mathematical advances in viral of substrate flow. The effects of fluid motion and experimental research because of their infection modeling and resulting insights on fronts in the general advection-reaction- unique, adaptive dynamical properties. into viral infections, at both the within-host diffusion (ARD) case have only recently Strongly nonlinear dispersive media may and between-hosts (epidemiological) scales. received significant attention, despite the wide exhibit quite intriguing phenomena such applicability of ARD, including microfluidic as broadband absorption, high-rate wave Organizer: Jessica M. Conway chemical reactors, plasmas, ecosystem attenuation and strong energy localization, Pennsylvania State University, USA dynamics in the oceans (e.g., plankton rendering them highly attractive for Organizer: Naveen K. Vaidya blooms), cellular- and embryonic-scale multiple engineering applications. In this University of Missouri, Kansas City, biological processes. This minisymposium minisymposium, leading experts dealing brings together groups studying ARD systems USA with this class of dynamical systems will from a variety of perspectives, including come together for a creative exchange of 1:30-1:55 Modeling HCV Infection: experiments, dynamical systems theory, ideas involving fundamental and applied Viral Dynamics and Genotypic numerical PDEs, and analytics. research. Diversity Organizer: Kevin A. Mitchell Ruy M. Ribeiro, Los Alamos National Organizer: Anna Vainchtein University of California, Merced, USA University of Pittsburgh, USA Laboratory, USA Organizer: Thomas H. Solomon Organizer: Yuli Starosvetsky 2:00-2:25 HIV Viral Rebound Times Following Suspension of Art: Bucknell University, USA Technion - Israel Institute of Stochastic Model Predictions Organizer: John R. Mahoney Technology, Israel Jessica M. Conway, Pennsylvania State University of California, Merced, USA 1:30-1:55 Nonlinear Dynamics of University, USA Non-Stretched Membrane 1:30-1:55 The Domain Dependence 2:30-2:55 Modeling HIV Infection of Chemotaxis in a Two-Dimensional Leonid Manevich, Russian Academy of Dynamics under Conditions of Drugs Turbulent Flow Sciences, Russia of Abuse Kimberley Jones and Wenbo Tang, Arizona 2:00-2:25 Discrete Breathers in Vibro- Naveen K. Vaidya, University of Missouri, State University, USA Impact Lattice Models Kansas City, USA 2:00-2:25 Flow and Grow: Experimental Itay Grinberg and Oleg Gendelman, 3:00-3:25 Modeling Equine Infectious Studies of Time-Dependent Reaction- Technion Israel Institute of Technology, Anemia Virus Infection: Virus Diffusion-Advection Systems Israel Dynamics, Immune Control, and Douglas H. Kelley, University of Rochester, 2:30-2:55 Mixed Solitary – Shear Escape USA Waves in a Granular Network Elissa Schwartz, Washington State 2:30-2:55 Lagrangian Coherent Yijing Zhang, University of Illinois at University, USA Structures for Reaction Fronts in Urbana-Champaign, USA; Md. Arif Unsteady Flows Hasan, University of Illinois, USA; Yuli Kevin A. Mitchell and John R. Mahoney, Starosvetsky, Technion - Israel Institute of University of California, Merced, USA Technology, Israel; D. Michael McFarland and Alexander Vakakis, University of 3:00-3:25 Transport in Chaotic Fluid Illinois, USA Convection 3:00-3:25 Stable Two-Dimensional Mark Paul, Virginia Tech, USA Solitons in Free Space: Gross- Pitaevskii Equations with the Spin- Orbit Coupling Boris Malomed, Tel Aviv University, Israel 2015 SIAM Conference on Applications of Dynamical Systems 67

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS100 MS101 MS102 Nonsmooth Dynamical Models from Data Complex Network Theory Systems: Theory and 1:30 PM-3:30 PM Based Approaches in Applications - Part II of II Room:White Pine the Analyses of Complex 1:30 PM-3:30 PM Data modeling uses a model to represent a Systems and Data - Room:Superior B possibly large data set with a much smaller Part II of II set of rules. The type of model depends on 1:30 PM-3:00 PM For Part 1 see MS87 the goal of the modeling; data assimilation Many physical systems involve abrupt events, techniques can be used to create predictive Room:Primrose A such as switches, impacts or thresholds, models. If one wants to discover the and are well-modelled by equations that are For Part 1 see MS89 structure of the data set, manifold learning Analysis of network data obtained from a nonsmooth. This minisymposium will discuss techniques can reveal that a data set that novel applications of nonsmooth systems in complex system is often a challenging task. appears high dimensional actually exists In this minisymposium we will be discussing ecology, optics and neuroscience, as well as on a low dimensional manifold. Both types describe new developments in the theory of few novel approaches for obtaining insights of modeling seek simple descriptions of into the structural and functional properties nonsmooth systems. Overall the talks will complicated data sets. highlight the various nuances of nonsmooth of empirical networks and networks inferred systems and show how these relate to the Organizer: Thomas L. Carroll from data. One of our focus areas will be to dynamical behaviour of the physical systems Naval Research Laboratory, USA employ simulation of variety of dynamical being modelled. processes on networks to study properties 1:30-1:55 Nonlinear Dynamics of of empirical networks. We will also discuss Organizer: David J. Simpson Variational Data Assimilation methodologies to overcome problems in Massey University, New Zealand Henry D. Abarbanel, Kadakia Nirag, the analysis of empirical networks due to Jingxin Ye, Uriel I. Morone, and Daniel 1:30-1:55 Lost in Transition: spurious or missing links. Dynamical system Rey, University of California, San Diego, Nonlinearities in the Dynamics of based approaches for transforming data USA Switching into a network representing will also be Mike R. Jeffrey, University of Bristol, 2:00-2:25 Precision Variational presented. United Kingdom Approximations in Statistical Data Organizer: Nishant Malik Assimilation 2:00-2:25 Some Nonsmooth Problems University of North Carolina at Chapel Jingxin Ye, University of California, San Inspired by Conceptual Climate Hill, USA Diego, USA Models 1:30-1:55 Shadow Networks: Anna M. Barry, University of British 2:30-2:55 Manifold Learning Discovering Hidden Nodes with Columbia, Canada Approach for Modelling Collective Models of Information Flow Chaos in High-Dimensional James Bagrow, University of Vermont, 2:30-2:55 Grazing Bifurcations in Dynamical Systems Engineering and Medical Systems USA Hiromichi Suetani, Kagoshima University, Marian Wiercigroch, University of Japan 2:00-2:25 A Network Measure for the Aberdeen, United Kingdom Analysis and Visualization of Large- 3:00-3:25 Attractor Comparisons Scale Graphs 3:00-3:25 Continuation of Chatter in a Based on Density Mechanical Valve Roldan Pozo, National Institute of Thomas L. Carroll, Naval Research Standards and Technology, USA Harry Dankowicz and Erika Fotsch, Laboratory, USA University of Illinois at Urbana- 2:30-2:55 Revealing Collectivity in Champaign, USA; Alan R. Champneys, Evolving Networks: A Random Matrix University of Bristol, United Kingdom Theory Approach Saray Shai, University of North Carolina at Chapel Hill, USA 68 2015 SIAM Conference on Applications of Dynamical Systems

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS103 MS119 MT2 Transfer Operator Methods: From Singular Perturbation Stochastic Dynamics of Rare Geometry, Continuous Theory to some Slow-Fast Events Time, Infinite Dimensions, Systems: A Taste 4:00 PM-6:00 PM Fast Computation 1:30 PM-3:30 PM Room:Ballroom III 1:30 PM-3:30 PM Room:Wasatch B Chair: Eric Forgoston, Montclair State Room:Primrose B Geometric Singular Perturbation Theory and University, USA the rôle of an small parameter in Fast-Slow Transfer operators are global descriptors Noise plays a fundamental role in a wide systems permit to decompose the dynamics of ensemble evolution under nonlinear variety of physical and biological dynamical and to analyse global changes and bifurcations dynamics and efficient methods of systems. The noise may be internal or when such parameter decreases. Besides, computing coherent structures and attractors. external - internal noise is inherent to the Singular Perturbation Theory is closely related The speakers will describe advances in four system itself and arises due to the random to problems concerning persistence of homo/ areas. First, a new fundamental geometric interactions of a finite number of agents in heteroclinic connections, beyond-all-orders characterisation of finite-time coherent the system, while external noise arises from algebraic expansions and Stokes phenomenon. sets and its associated transfer operator. a source outside of the system. In recent The aim of this minisymposium is to offer a Second, new spectral theory and numerics years, researchers have identified situations very general (but partial) overview of some of for periodically-driven flows and their time- where even weak noise can induce a large these problems under both a theoretical and asymptotic coherent sets. Third, a transfer fluctuation that leads to population extinction, numerical viewpoints. operator approach to computing attractors switching between metastable states in for infinite-dimensional delay differential Organizer: J. Tomas Lazaro ecological systems, or the escape of a particle equations. Fourth, numerical methods for Universitat Politecnica de Catalunya, from a potential well. The purpose of this computing coherent sets for time-dependent Spain minitutorial is to expose the audience to the advection-diffusion equations. theory underlying the dynamics of rare events Organizer: Sergio Serrano for stochastic ODEs and PDEs along with a Organizer: Gary Froyland University of Zaragoza, Spain wide variety of applications. University of New South Wales, 1:30-1:55 Stokes Phenomenon in Australia Noise-Induced Rare Events: Switching, a Singularly Perturbed Differential Escape, and Extinction in Stochastic Organizer: Kathrin Padberg- Equation ODEs Gehle Vassili Gelfreich, University of Warwick, Eric Forgoston, Montclair State University, Dresden University of Technology, United Kingdom USA Germany 2:00-2:25 Homoclinic Orbits With Many Noise-Induced Rare Events: Failures 1:30-1:55 The Geometry of Loops Near a 02 iΏ Resonant Fixed and Exits in Stochastic Wave Lagrangian Coherent Structures Point Of Hamiltonian Systems Equations Gary Froyland, University of New South Tiphaine Jézéquel, University of Tours, Richard O. Moore, New Jersey Institute of Wales, Australia France; Patrick Bernard, CEREMADE Technology, USA Universite Paris 9 Dauphine, France; Éric 2:00-2:25 Coherent Families: Spectral Noise-Induced Rare Events: Lombardi, Universite Paul Sabatier, France Theory for Transfer Operators in Applications in Physical and Continuous Time 2:30-2:55 Canard Orbits and Mixed- Biological Sciences Peter Koltai, Free University of Berlin, Mode Oscillations in a Chemical Michael Khasin, NASA Ames Research Germany; Gary Froyland, University of Reaction Model Center, USA New South Wales, Australia Bernd Krauskopf, Jose Mujica, and Hinke M. Osinga, University of Auckland, New 2:30-2:55 On the Computation of Zealand Attractors for Delay Differential Equations 3:00-3:25 Symbolic Dynamical Michael Dellnitz, University of Paderborn, Unfolding of Spike-Adding Bifurcations Germany in Chaotic Neuron Models Roberto Barrio, University of Zaragoza, 3:00-3:25 Computing Coherent Sets in Spain; Marc Lefranc, PHLAM - Universite Turbulent Systems de Lille, France; M. Angeles Martinez and Andreas Denner, Technische Universitaet Sergio Serrano, University of Zaragoza, Muenchen, Germany; Oliver Junge, Spain University of Paderborn, Germany Coffee Break 3:30 PM-4:00 PM Room:Golden Cliff 2015 SIAM Conference on Applications of Dynamical Systems 69

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS104 MS105 MS106 Featured Minisymposium: Featured Minisymposium: Featured Minisymposium: Non-Autonomous Random Walks, First Passage Time-Delayed Feedback Instabilities Time and Applications 4:00 PM-6:00 PM 4:00 PM-6:00 PM 4:00 PM-6:00 PM Room:Wasatch B Room:Ballroom I Room:Ballroom II Time-delayed feedback is a simple and powerful method for influencing and In many applications from the natural Numerous problems -- from the molecular controlling complex nonlinear systems. sciences and engineering aperiodic external to macroscopic scales -- involve strategies In its simplest form, the method has been forcing often leads to interesting nonlinear based on random (possibly biased) walks. successfully used to control unstable periodic phenomena that can be characterised as non- Examples range from fast-folding DNA orbits in dynamical models arising for autonomous instabilities. Such instabilities strands, to predator-prey interactions and instance in engineering, physics or biology. are mathematically challenging and often search and rescue operations. In this featured More recently, the scope of time-delayed puzzle scientists because they cannot, owing symposium, we present novel results in the feedback has been expanded to systems to their transient or finite-time nature, be field that also show the diversity and beauty with multiple delay and the connection with explained using traditional bifurcation of the subject. The proposed speakers are fixed point problems has been clarified. In theory. This minisymposium highlights world-renowned experts that will present new this minisymposium we will cover these recent techniques to analyse stability of applications to problems in cellular biology, new developments and discuss applications non-autonomous ODEs and PDEs, with chemistry, statistical mechanics, neuroscience of time delay to climate systems and cluster applications to rate-induced tipping points, and even sports. The topics of this session synchronisation failure boundaries in earthquake engineering unify various approaches used, offering and finite-time transport in (ocean) surface unique perspectives to reach and inform a Organizer: Andreas Amann flows. wide target audience. University College Cork, Ireland Organizer: Sebastian M. Organizer: Theodore Kolokolnikov 4:00-4:25 Pattern Formation in Wieczorek Dalhousie University, Canada Systems with Multiple Delayed University College Cork, Ireland Feedbacks Organizer: Sidney Redner Serhiy Yanchuk, Humboldt University at 4:00-4:25 Rate-Induced Bifurcations in Santa Fe Institute, USA Slow-Fast Systems Berlin, Germany 4:00-4:25 First Passage Time Problems Sebastian M. Wieczorek, University 4:30-4:55 Connection Between for Stochastic Hybrid Systems College Cork, Ireland Extended Time-Delayed Feedback , University of Utah, USA Paul C. Bressloff and Nonlinear Fixed-Point Problems 4:30-4:55 Interactions Between Noise and University of Oxford, United Kingdom and Rate-Induced Tipping Jan Sieber, University of Exeter, United 4:30-4:55 Exploration and Trapping of Kingdom Paul Ritchie, University of Exeter, United Mortal Random Walkers Kingdom 5:00-5:25 Interplay of Adaptive , University of Katja Lindenberg Topology and Time Delay in the 5:00-5:25 A Direct Method for California, San Diego, USA; Santos B. Control of Cluster Synchronization Computing Failure Boundaries of Yuste and Enrique Abad, Universidad de Judith Lehnert, Technische Universität Non-autonomous Systems Extremadura, Spain Berlin, Germany; Alexander Fradkov, Hinke M. Osinga, University of Auckland, 5:00-5:25 Trajectory-to-Trajectory St. Petersburg State University, Russia; New Zealand Fluctuations in the First-Passage Eckehard Schöll and Philipp Hövel, 5:30-5:55 Finite-Time Lagrangian Phenomena in Bounded Domains Technische Universität Berlin, Germany; Transport Through Surfaces in Gleb Oshanin, Laboratoire de Physique Anton Selivanov, St. Petersburg State Volume-Preserving Flows Théorique de la Matière Condensée, France University, Russia Daniel Karrasch, ETH Zürich, Switzerland 5:30-5:55 Application of First-Passage 5:30-5:55 Bifurcation Analysis of Ideas to the Statistics of Lead a Model for the El Nño Southern Changes in Basketball Oscillation Sidney Redner, Santa Fe Institute, USA; Andrew Keane, Bernd Krauskopf, and Aaron Clauset, University of Colorado Claire Postlethwaite, University of Boulder, USA; Marina Kogan, University Auckland, New Zealand of Colorado, USA 70 2015 SIAM Conference on Applications of Dynamical Systems

Wednesday, May 20 Wednesday, May 20 Wednesday, May 20 MS107 MS108 MS109 Featured Minisymposium: Featured Minisymposium: Featured Minisymposium: Emerging Strategies Invariant Manifolds Medical Applications for Stability Analysis of Unravelling Complicated 4:00 PM-6:00 PM Electrical Power Grids Dynamics Room:Primrose B 4:00 PM-6:00 PM 4:00 PM-6:00 PM In recent years, there has been growing Room:Maybird Room:Primrose A interest in employing ideas from dynamical systems and control theory for medical The so-called swing equations which Global invariant manifolds of maps and applications. This minisymposium will describe the course grained dynamics on an vector fields undergo critical re-arrangements emphasize recent theoretical and experimental electrical power grid are highly non-linear under parameter variation. These topological advances in the way such approaches may with a solution space that grows with the and geometric transitions may result in be used to both understand and combat the size of the grid. Due to their rich dynamics, drastic changes of the global dynamics. underlying mechanisms of dysfunction that the equations have been the subject of Typically, major changes to invariant can occur for specific diseases. We include intense research using a wide range of manifolds may trigger the onset of chaos, a broad sampling of speakers representing techniques. This minisymposium focuses transformation or creation of basins of applications from the fields of cardiology, on the global structure of these equations attraction, the formation of homo- and neuroscience, and diabetes research. and develops new approaches to study the heteroclinic orbits and, ultimately, the system stability by using a combination of reorganization of the overall structure of the Organizer: Dan D. Wilson tools such as power flow approximations, phase space. The aim of this minisymposium University of California, Santa Barbara, USA bifurcation theory, Lyapunov functions is to present recent advances and discuss new Organizer: Jeff Moehlis and stochastic methods. The speakers challenges in the way invariant manifolds University of California, Santa Barbara, USA will discuss their latest results in this can be used as a tool to understand area and present examples of relevance in complicated global phenomena. 4:00-4:25 Termination of Cardiac applications. Alternans Using Isostable Response Organizer: Stefanie Hittmeyer Curves Organizer: Lewis G. Roberts University of Auckland, New Zealand Dan D. Wilson and Jeff Moehlis, University University of Bristol, United Kingdom Organizer: Pablo Aguirre of California, Santa Barbara, USA Organizer: Florian Dorfler Universidad Técnica Federico Santa 4:30-4:55 Unification of Neuronal ETH Zürich, Switzerland María, Chile Spikes, Seizures, and Spreading 4:00-4:25 A Parametric Investigation 4:00-4:25 Bifurcations of Generalised Depression of Rotor Angle Stability Using Direct Julia Sets Near the Complex Steven J. Schiff, Pennsylvania State Methods Quadratic Family University, USA; Yina Wei, University of Lewis G. Roberts, Alan R. Champneys, and Stefanie Hittmeyer, Bernd Krauskopf, and California, Riverside, USA; Ghanim Ullah, Mario Di Bernardo, University of Bristol, Hinke M. Osinga, University of Auckland, University of South Florida, USA United Kingdom; Keith Bell, University of New Zealand 5:00-5:25 Therapeutic Mechanisms Strathclyde, United Kingdom 4:30-4:55 Parameterization Method of High Frequency DBS in Parkinson’s 4:30-4:55 Voltage Stability in Power for Local Stable/unstable Manifolds of Disease: Neural Restoration Through Networks and Microgrids Periodic Orbits Loop-Based Reinforcement Florian Dorfler, ETH Zürich, Switzerland; Jason Mireles James, Rutgers University, Sridevi Sarma, Johns Hopkins University, John Simpson-Porco, University of USA USA; Sabato Santaniello, University of Colorado Boulder, USA California, USA; Francesco Bullo, 5:00-5:25 A Global Bifurcation of University of California, Santa Barbara, Mixed-mode Oscillations 5:30-5:55 Perspectives on Theories USA Ian M. Lizarraga and John Guckenheimer, of Diabetogenesis and Glucose 5:00-5:25 Finding Useful Statistical Cornell University, USA Management Indicators of Instability in Pranay Goel, Indian Institute for Science 5:30-5:55 Practical Stability Versus Stochastically Forced Power Systems Education and Research, Pune, India; Diffusion in the Spatial Restricted Saroj Ghaskadbi, Savitribai Phule Pune Goodarz Ghanavati, Paul Hines, and Taras Three-body Problem Lakoba, University of Vermont, USA University, India Maisa O. Terra, Technological Institute 5:30-5:55 Synchronization Stability of of Aeronautics, Brazil; Carles Simó, Lossy and Uncertain Power Grids University of Barcelona, Spain; Priscilla Konstantin Turitsyn and Thanh Long Vu, de Sousa-Silva, Technological Institute of Dinner Break Massachusetts Institute of Technology, Aeronautics, Brazil USA 6:00 PM-8:30 PM Attendees on their own 2015 SIAM Conference on Applications of Dynamical Systems 71

Wednesday, May 20 Slow-fast Analysis of Earthquake Feasibility of Binding Heteroclinic Faulting Networks PP2 Elena Bossolini, Kristian Uldall Xue Gong, Ohio University, USA; Valentin Kristiansen, and Morten Brøns, Technical Afraimovich, Universidad Autonoma de San Poster Session and Dessert University of Denmark, Denmark Luis Potosi, Mexico Reception Quasicycles in the Stochastic Hybrid Dynamic Square Patterns in 2D Neural 8:30 PM-10:30 PM Morris-Lecar Neural Model Fields Heather A. Brooks, University of Utah, Kevin R. Green and Lennaert van Veen, Room:Ballroom USA; Paul C. Bressloff, University of University of Ontario Institute of Intermittent Synchronization/ Utah, USA and University of Oxford, Technology, Canada desynchronization in Population United Kingdom Dynamics Controllability of Brain Networks Computation of Normally Hyperbolic Shi Gu, University of Pennsylvania, USA; Sungwoo Ahn, Arizona State University, Invariant Manifolds USA; Leonid Rubchinsky, Indiana Fabio Pasqualetti, University of California, Marta Canadell, Georgia Institute of University - Purdue University Riverside, USA; Matthew Ceislak and Technology, USA; Alex Haro, Universitat Indianapolis, USA Scott Grafton, University of California, de Barcelona, Spain Santa Barbara, USA; Danielle S. Bassett, Parabolic Bursting in Inhibitory Neural A Novel Speech-Based Diagnostic University of Pennsylvania, USA Circuits Test for Parkinson’s Disease Compressive Sensing with Exactly Deniz Alacam and Andrey Shilnikov, Integrating Machine Learning Georgia State University, USA Solvable Chaos with Web and Mobile Application Sidni Hale, Anthony DiPofi, and Bradley An Accurate Computation of the Development for Cloud Deployment Kimbrell, Radix Phi, USA Tangent Map for Computation of Pooja Chandrashekar, Thomas Jefferson Lagrangian Coherent Structures High School of Science and Techonology, Identifying the Role of Store-Operated Siavash Ameli and Shawn Shadden, USA Calcium Channels in Astrocytes Via An University of California, Berkeley, USA Open-Cell Model An Agent-Based Model for mRNA Gregory A. Handy, Alla Borisyuk, Marsa Nonlinear Dynamics in Coupled Localization in Frog Oocytes Taheri, and John White, University of Utah, Semiconductor Laser Network Veronica M. Ciocanel and Bjorn USA Implementations Sandstede, Brown University, USA Apostolos Argyris, Michail Bourmpos, Behavioral Dynamics and STD Effects of Stochastic Gap-Junctional Transmission Alexandros Fragkos, and Dimitris Coupling in Cardiac Cells and Tissue Syvridis, National & Kapodistrian Michael A. Hayashi and Marisa Eisenberg, William Consagra, Rochester Institute of University of Athens, Greece University of Michigan, USA Technology, USA Symplectic Maps with Reversed Master Stability Functions for the Fixed Maximizing Plant Fitness Under Current in a Tokamaks Point Solution of Synchronized Identical Herbivore Attack Bruno Bartoloni and Ibere L. Caldas, Systems with Linear Delay-Coupling Karen M. Cumings, Peter R. Kramer, and and a Single Constant Delay University of Sao Paulo, Brazil Bradford C. Lister, Rensselaer Polytechnic Stanley R. Huddy and Jie Sun, Clarkson Analysis of Spatiotemporal Institute, USA University, USA Dynamical Systems from Multi- The Derivation of Mass Action Laws: Attribute Satellite Images Windows of Opportunity: Issues and Questions Ranil Basnayake and Erik Bollt, Clarkson Synchronization in On-Off Stochastic Jonathan Dawes, University of Bath, Networks University, USA; Nicholas Tufillaro, United Kingdom; Max O. Souza, Oregon State University, USA; Jie Sun, Russell Jeter and Igor Belykh, Georgia State Universidade Federal Fluminense, Brazil Clarkson University, USA University, USA Heterogeneity and Oscillations in Phase Response Analysis of the Two-Theta Neuron: Phase Models for Small Predator-Prey Swarms Circadian Clock in Neurospora Bursting Networks Jeff Dunworth and Bard Ermentrout, Crassa Aaron Kelley, Georgia State University, USA University of Pittsburgh, USA Jacob Bellman, University of Cincinnati, Canard-Mediated Dynamics in a USA Bacterial Disinfection with the Phantom Burster Presence of Persisters Time Series Based Prediction of Elif Köksal Ersöz, Mathieu Desroches, Sepideh Ebadi, Florida State University, Extreme Events in High-Dimensional Maciej Krupa, and Frédérique Cleément, USA Excitable Systems INRIA Paris-Rocquencourt, France Stephan Bialonski, Max Planck Institute Chaotic Mixing in a Curved Channel A Mathematical Model for Adaptive for Dynamics of Complex Systems, with Slip Surfaces Crawling Locomotion Germany; Gerrit Ansmann, University Piyush Garg, Indian Institute of Shigeru Kuroda and Toshiyuki Nakagaki, of Bonn, Germany; Holger Kantz, Max Technology Roorkee, India; Jason R. Hokkaido University, Japan Planck Institute for Physics of Complex Picardo and Subramaniam Pushpavanam, Systems, Germany Indian Institute of Technology Madras, India continued in next column continued in next column continued on next page 72 2015 SIAM Conference on Applications of Dynamical Systems

Wednesday, May 20 Capacity for Learning the Shape of Osteocyte Network Formation Arena in the Single-Celled Swimmer, Jake P. Taylor-King, Mason A. Porter, PP2 Viewed from Slow Dynamics of and Jon Chapman, University of Oxford, Membrane Potential United Kingdom; David Basanta, H. Poster Session and Dessert Toshiyuki Nakagaki and Itsuki Kunita, Lee Moffitt Cancer Center & Research Reception Hokkaido University, Japan; Tatsuya Institute, USA Yamaguchi, Kyushu University, Japan; On a FitzHugh-Nagumo Kinetic 8:30 PM-10:30 PM Masakazu Akiyama, Hokkaido University, Model for Neural Networks Japan; Atsushi Tero, Kyushu University, Room:Ballroom Cristobal Quininao, Laboratoire Jacques- Japan; Shigeru Kuroda and Kaito Ooki, Louis Lions, France; Jonathan D. cont. Hokkaido University, Japan Touboul, Collège de France, France; Co-Dimension Two Bifurcations Stéphane Mischler, Universite Paris 9 Effective Dispersion Relation of the in Piecewise-Smooth Continuous Dauphine, France Dynamical Systems Nonlinear Schrödinger Equation Examining Partial Cascades in Katelyn J. Leisman and Gregor Kovacic,ˇ ˇ Wilten Nicola and Sue Ann Campbell, Clustered Networks with High Rensselaer Polytechnic Institute, University of Waterloo, Canada Intervertex Path Lengths USA; David Cai, Courant Institute Analysis of Malaria Transmission Yosef M. Treitman and Peter R. Kramer, of Mathematical Sciences, New York Dynamics with Saturated Incidence Rensselaer Polytechnic Institute, USA University, USA Samson Olaniyi, Ladoke Akintola Almost Complete Separation of a Mathematical Model of Bidirectional University of Technology, Nigeria Fluid Component from a Mixture Vesicle Transport and Sporadic Temporally Periodic Neural Using the Burgers Networks of Micro- Capture in Axons Responses from Spatially Periodic separators Ethan Levien, University of Utah, USA; Stimuli Shinya Watanabe, Ibaraki University, Paul C. Bressloff, University of Utah, Jason E. Pina and Bard Ermentrout, Japan; Sohei Matsumoto, National USA and University of Oxford, United University of Pittsburgh, USA Institute of Advanced Industrial Science Kingdom and Technology, Japan; Tomohiro Using a Stochastic Field Theory to Higurashi, Yuya Yoshikawa, and Naoki Modelocking in Chaotic Advection- Understand Collective Behavior of Ono, Shibaura Institute of Technology, Reaction-Diffusion Systems Swimming Microorganisms Japan Rory A. Locke, John R. Mahoney, Yuzhou Qian, Peter R. Kramer, and and Kevin A. Mitchell, University of Patrick Underhill, Rensselaer Polytechnic New Data Anysis Approach for California, Merced, USA Institute, USA Complex Signals with Low Signal to Noise Ratio’s Effect of Multi-Species Mass Consensus and Synchronization over Jeremy Wojcik, Georgia State University, Emergence on Biodiversity Biologically-Inspired Networks: From USA James E. McClure and Nicole Abaid, Collaboration to Antagonism Virginia Tech, USA Subhradeep Roy and Nicole Abaid, Data Assimilation for Traffic State and A B Cell Receptor Signaling Model Virginia Tech, USA Parameter Estimation Chao Xia, Bjorn Sandstede, and Paul and Dynamic Origins of Cell Oscillatory Shear Flow Influence on Carter, Brown University, USA; Laura Response the Two Point Vortex Dynamics Slivinski, Woods Hole Oceanographic Reginald Mcgee, Purdue University, USA Evgeny Ryzhov and Konstantin Koshel, Institute, USA Stability of Morphodynamic Equilibria Pacific Oceanological Institute of the in Tidal Basins Russian Academy of Sciences, Russia Stochastic Active-Transport Model of Cell Polarization Corine J. Meerman and Vivi Rottschäfer, Wild Dynamics in Nonlinear Bin Xu, University of Utah, USA; Paul C. Leiden University, Netherlands; Henk Integrate-and-Fire Neurons: Mixed- Bressloff, University of Utah, USA and Schuttelaars, Delft University of Mode Bursting, Spike Adding and Technology, Netherlands Chaos University of Oxford, United Kingdom Frequency-Dependent Left-Right Justyna H. Signerska, INRIA, France; Statistical Properties of Finite Systems Coordination in Locomotor Pattern Jonathan D. Touboul, Collège de France, of Point-Particles Interacting Through Generation France; Alexandre Vidal, University of Binary Collisions Yaroslav Molkov, Indiana University - Evry-Val-d’Essonne, France Alexander L. Young, Joceline Lega, and Sunder Sethuraman, University of Purdue University Indianapolis, USA; Return Times and Correlation Decay Arizona, USA Bartholomew Bacak, Drexel University in Linked Twist Maps College of Medicine, USA; Ilya A. Rybak, Rob Sturman, University of Leeds, United Drexel University, USA Kingdom

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Heteroclinic Separators of Magnetic Thursday, May 21 Fields in Electrically Conducting Fluids Thursday, May 21 Evgeny Zhuzhoma, National Research MS111 University Higher School of Economics, Recent Insights into Russia; Vyatcheslav Grines and Timur Registration Medvedev, Lobachevsky State University Controling Flow Structures - of Nizhny Novgorod, Russia; Olga 8:00 AM-4:45 PM Part I of II Pochinka, National Research University Room:Ballroom Foyer Higher School of Economics, Russia 8:30 AM-10:30 AM Equivalent Probability Density Room:Ballroom II Moments Determine Equivalent For Part 2 see MS124 Epidemics in An Sirs Model with MS110 Interior flow entities such as fluid interfaces, Temporary Immunity coherent structures and invariant manifolds Thomas W. Carr, Southern Methodist Effective Multiscale have a profound influence on transport in University, USA Computational Modeling of unsteady flows. The ability to control them is Waveaction Spectra for Fully Spatio-temporal Systems attracting much recent interest, fueled in part Nonlinear MMT Model by emerging biotechnological applications at Michael Schwarz, Gregor Kovacic, and 8:30 AM-10:30 AM the microfluidic level. This minisymposium Peter R. Kramer, Rensselaer Polytechnic Room:Ballroom I will cover a range of state-of-the-art Institute, USA; David Cai, Shanghai approaches to controling flow structures Across science and engineering many Jiao Tong University, China and Courant which are inspired by dynamical systems systems are only realistically described by Institute of Mathematical Sciences, New methods. models on multiple spatial and temporal York University, USA scales. Such multiscale systems are Organizer: Sanjeeva Balasuriya Rigorous Numerics for Analytic notoriously complex and computationally University of Adelaide, Australia Solutions of Differential Equations: The demanding. In developing the desired Organizer: Marko Budisic Radii Polynomial Approach ‘coarse-grained’ or macroscale model, University of Wisconsin, Madison, USA Allan R. Hungria, University of Delaware, major concerns are the efficiency of the USA; Jean-Philippe Lessard, Université the macroscale modelling and its accuracy. Organizer: Jean-Luc Thiffeault Laval, Canada; Jason Mireles-James, We discuss recent developments in the University of Wisconsin, Madison, USA Florida Atlantic University, USA computational modelling of the emergent 8:30-8:55 Control of Thin-Layer Flows dynamics of multiscale systems. with Patterned Surfaces Organizer: Anthony J. Roberts Jean-Luc Thiffeault, University of University of Adelaide, Australia Wisconsin, Madison, USA; Jay Johnson, University of Texas at Austin, USA 8:30-8:55 Better Buffers for Patches in Macroscale Simulation of Systems 9:00-9:25 Mesohyperbolicity, Mix- with Microscale Randomness Norm and the Hunt for Mh370 Anthony J. Roberts, University of Sophie Loire and Hassan Arbabi, University Adelaide, Australia of California, Santa Barbara, USA; Stefan Ivic, Rijeka University, Croatia; Patrick 9:00-9:25 Resilient Algorithms for Clary, University of California, Santa Reconstructing and Simulating Barbara, USA; Bojan Crnkovic and Nelida Gappy Flow Fields in CFD Crnjaric-Zic, Rijeka University, Croatia; , Brown University, USA; Seungjoon Lee Igor Mezic, University of California, Santa Ioannis Kevrekedis, Princeton University, Barbara, USA USA; George E. Karniadakis, Brown University, USA 9:30-9:55 Triggers of Rogue Waves in Deep Water Envelope Equations Will Cousins and Themistoklis Sapsis, Massachusetts Institute of Technology, USA 10:00-10:25 Boundary Conditions and the Linking of Computational Domains in Patch Dynamics Schemes I. G. Kevrekidis, Princeton University, USA

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Thursday, May 21 Thursday, May 21 Thursday, May 21 MS111 MS112 MS113 Recent Insights into Dynamical Systems Aspects Statistical Physics and Controling Flow Structures - of Legged Locomotion Nonlinear Dynamics for the Part I of II 8:30 AM-10:30 AM Earth’s Cryosphere 8:30 AM-10:30 AM Room:Ballroom III 8:30 AM-10:30 AM Room:Ballroom II The purpose of this minisymposium is to Room:Magpie A review the state of the art in biomechanical Important elements of the Earth’s cont. and neural modelling of legged locomotion. Cryosphere such as sea ice, permafrost and Topics covered will include interaction snow were formed under temperature change between central pattern generators and resulting in nonlinear phase transitions. 9:30-9:55 Closed-Loop Control of muscles, experimental observation of human These critical phenomena in the Earth’s Complex and Turbulent Flows Using subjects on steady and moving ground, Cryosphere remain of continuing interest as Machine Learning Control: a Reverse cross-species comparison, stability, basins of the climate system warms, and are crucial Engineering Approach attraction, gait transition, feedback control for the stability of the climate system. The Thomas Duriez, Buenos Aires University, and reduced-order models. melting processes in the Earth’s Cryosphere Argentina; Vladimir Parezanovic, Kai Von Organizer: Shinya Aoi can be investigated through classical Krbek, Jean-Paul Bonnet, Laurent Cordier, Kyoto University, Japan statistical physics models as well the and Bernd R. Noack, CNRS, France; Marc nonlinear behaviour of the climate system Segond and Markus W Abel, Ambrosys Organizer: Alan R. Champneys caused by phase transitions can be described GmbH, Germany; Nicolas Gautier and University of Bristol, United Kingdom with help of standard nonlinear dynamics Jean-Luc Aider, CNRS, France; Cedric 8:30-8:55 What Can Coupled, tools. Raibaudo, Christophe Cuvier, and Michel Nonlinear Oscillators Say About Noisy, Organizer: Ivan Sudakov Stanislas, École Centrale de Lille, France; Perturbed Cockroaches University of Utah, USA Antoine Debien, Nicolas Mazellier, and Philip Holmes, Princeton University, USA Azeddine Kourta, Universite d’Orleans, 8:30-8:55 Statistical Physics Models 9:00-9:25 Formation Mechanism for France; Steven Brunton, University of for Critical Phenomena in Permafrost Basin of Attraction of Bipedal Working Washington, USA Lakes Models Ivan Sudakov, University of Utah, USA 10:00-10:25 Controlling Hyperbolic Obayashi Ippei, Kyoto University, Japan Trajectories and Invariant Manifolds 9:00-9:25 The Evolution of Complexity in Flows 9:30-9:55 Experimental Observation of in Arctic Melt Ponds: a Statistical Rhythm Control of Human Gait Using Sanjeeva Balasuriya, University of Physics Perspective Moving Floor Adelaide, Australia; Kathrin Padberg- Yiping Ma, University of Colorado Boulder, , University of Electro- Gehle, Dresden University of Technology, Tetsuro Funato USA Communications, Japan; Shinya Aoi, Germany Nozomi Tomita, and Tsuchiya Kazuo, 9:30-9:55 How Climate Model Kyoto University, Japan Complexity Impacts the Stability of the Sea Ice Cover 10:00-10:25 Lateral Balance of Till Wagner, University of California, Human Walking and Human Structure San Diego, USA; Ian Eisenman, Scripps Interaction Institution of Oceanography, USA John Macdonald, Jeremy Burn, Matteusz Bocian, and Alan R. Champneys, 10:00-10:25 Growth and Fluctuations University of Bristol, United Kingdom of Suncups on Alpine Snowpacks: Comparison of Field Observations with a Nonlinear Pde Model Tom Tiedje, University of Victoria, Canada; Kevin A. Mitchell, Simon Fraser University, Canada 2015 SIAM Conference on Applications of Dynamical Systems 75

Thursday, May 21 Thursday, May 21 Thursday, May 21 MS114 MS115 MS117 Mathematical Modeling of Inverse Problems in Network Complex Collective Basal Ganglia Dynamics - Part I of II Dynamics of Oscillator 8:30 AM-10:30 AM 8:30 AM-10:30 AM Networks - Part I of II Room:Magpie B Room:Wasatch A 8:30 AM-10:30 AM Basal ganglia is a set of subcortical brain For Part 2 see MS127 Room:Maybird structures involved in many different Network Dynamics constitutes a rapidly For Part 2 see MS129 functions, including reinforcement learning expanding field with applications in natural Considerable progress has recently been and control of cognitive and motor and social science, medicine, engineering, made in understanding the collective programs. The impairment of the basal and beyond. Commonly, mathematical dynamics of large oscillator networks. ganglia may lead to different disorders scientists study how a specific network New analytical tools have been created including Parkinson’s disease. The objective model behaves collectively as a function and extended in their applicability, and of this minisymposium is to present together of parameters or inputs. Here, taking a novel effects have been demonstrated not moderns developments in the basal ganglia complementary view, we ask what recorded only theoretically and numerically, but modeling in application to different aspects time series from a network’s units and also experimentally. Results in this field of basal ganglia function and dysfunction, respective correlation and information have broad application to both physical such as dynamic patterns of activity in the measures tell us about the units’ local and biological systems. Part one of this basal ganglia, deep brain stimulation of dynamics and their real physical interactions. symposium will report recent general the basal ganglia, and interaction of basal Such inverse network dynamics are much mean field results involving chimera states, ganglia with brain’s cortex. less explored and even less understood. The assortative networks, and generalizations of Organizer: Yixin Guo minisymposium features recent trends, from the classic Kuramoto model. Part two will foundations and applications in time series Drexel University, USA focus on networks of neuronal oscillators, analysis to models in physics and biology. their relationship to field models, and the Organizer: Leonid Rubchinsky Organizer: Michael Rosenblum dynamical consequences of connectivity. Indiana University - Purdue University University of Potsdam, Germany Indianapolis, USA Organizer: Paul So Organizer: Marc Timme George Mason University, USA 8:30-8:55 Cortical Impact on the Dynamics of Subthalamo-pallidal Max-Planck-Institute for Dynamics and Organizer: Arkady Pikovsky Networks Self-Organization, Germany University of Potsdam, Germany Leonid Rubchinsky and Sungwoo Ahn, 8:30-8:55 Data-Driven Network Organizer: Ernest Barreto Indiana University - Purdue University Inference: Achievements, Problems, George Mason University, USA Indianapolis, USA; Elizabeth Zauber, Possible Research Directions Indiana University, USA; Robert Worth, Klaus Lehnertz, University of Bonn, 8:30-8:55 Chimera States in Globally Indiana University, USA Germany Coupled Oscillators Arkady Pikovsky, Michael Rosenblum, and 9:00-9:25 Oscillations and Action 9:00-9:25 Data Based Modelling: Azamat Yeldesbay, University of Potsdam, Selection in a Multi-Channel Model Inferring the Direct Directed Network Germany of the Basal Ganglia Structure from Data Roman M. Borisyuk and Robert Merrison- Björn Schelter, University of Aberdeen, 9:00-9:25 On the Mechanical Origin Hort, Plymouth University, United United Kingdom; Marco Thiel, King’s of Chimera States Kingdom College, University of Aberdeen, United Erik A. Martens, University of Copenhagen, Denmark 9:30-9:55 Possible Mechanisms for Kingdom Generation of Beta Oscillations in 9:30-9:55 Topology Predicts 9:30-9:55 The Kuramoto Model Parkinson’s Disease Dynamics; Dynamics Constrain of Coupled Oscillators with a Alexander Pavlides, University of Oxford, Topology Bi-Harmonic Coupling Function United Kingdom; John Hogan, Bristol Srinivas Gorur-Shandilya, Yale Maxim Komarov, Potsdam University, Centre for Applied Nonlinear Mathematics University, USA Germany and University of Bristol, United 10:00-10:25 Mean Field Theory 10:00-10:25 Network Structure from Kingdom; Rafal Bogacz, University of of Assortative Networks of Phase Oxford, United Kingdom Responses of Time-invariants Mor Nitzan, Hebrew University of Oscillators 10:00-10:25 Identifying and Tracking Jerusalem, Israel; Jose Casadiego and Juan G. Restrepo, University of Colorado Transitions in Neural Spiking Marc Timme, Max-Planck-Institute Boulder, USA; Edward Ott, University of Dynamics in the Subthalamic for Dynamics and Self-Organization, Maryland, USA Nucleus of Parkinson’s Patients Germany Uri Eden, Boston University, USA 76 2015 SIAM Conference on Applications of Dynamical Systems

Thursday, May 21 Thursday, May 21 Thursday, May 21 MS118 MS120 MS121 Recent Advances on Stochastic Dynamics and Engineering Applications Multiple Timescale Their Applications - of Non-smooth Dynamics - Dynamics - Part I of II Part I of II Part I of II 8:30 AM-10:30 AM 8:30 AM-10:30 AM 8:30 AM-10:30 AM Room:Superior A Room:White Pine Room:Primrose A For Part 2 see MS130 For Part 2 see MS132 For Part 2 see MS133 Multiple timescales are ubiquitous in models Stochastic dynamical concepts are crucial Friction and impact are challenging research of real-world phenomena such as neuron in modelling the dynamical behavior of areas of engineering. These phenomena firing, laser dynamics, and climatic rhythms. dynamical systems under uncertainty. are commonly described by empirical Differential equations involving variables There are some theory results of the models, such as the coefficient of restitution evolving on distinct timescales yield rich and stochastic dynamics such as the stochastic or various friction models, including the notoriously hard mathematical questions. attractors, invariant manifolds, invariant Coulomb-Amontons’ law. Modelling contact This two-part minisymposium presents recent measures. However, the theory is restricted mechanics from first principles is almost results on singularly perturbed ODEs, which on some conditions. Applied science and impossible, each model needs some parameter is the most amenable paradigm for analysis engineering requires more stochastic fitting. Even when a model is available, one of multiple timescale phenomena. We will dynamical techniques. The objective might not be able to solve it due to various give a panorama of this topic, from theoretical of this minisymposium is to bring the mathematical singularities, where there is work on planar canard problems, in both bridge between the new theory methods no unique prediction. This minisymposium smooth and non-smooth vector fields (Part I), and approaches to stochastic dynamics in shows a number of applications where the to more application-driven studies of complex applications. ‘rough’ terrain of non-smooth dynamics must oscillations with at least three variables and Organizer: Xiaopeng Chen be carefully navigated. Attempts will be also made to resolve singularities and identify two or more timescales (Part II). Peking University, China contact force models. Organizer: Mathieu Desroches Organizer: Jinqiao Duan Organizer: Robert Szalai INRIA Paris-Rocquencourt, France Illinois Institute of Technology, USA University of Bristol, United Kingdom Organizer: Vivien Kirk 8:30-8:55 Slow Manifolds and 8:30-8:55 Exploring Experimental Paths University of Auckland, New Zealand Interface Motion for Stochastic PDEs for Reliable Mathematical Models of Organizer: Jonathan E. Rubin Dirk Blömker, Universität Augsburg, Friction Germany University of Pittsburgh, USA Thibaut Putelat, University of Bristol, 8:30-8:55 Theoretical Analysis of 9:00-9:25 Slow Manifolds for a United Kingdom Nonlocal Spde Homoclinic Canards 9:00-9:25 Painlevé Paradox: Lessons Jean-Pierre Francoise, Universite Pierre et Lu Bai, Huazhong University of Science & That We Do Not Learn from Simple Marie Curie (Paris 6), France Technology, China Examples 9:00-9:25 Singular Bogdanov-Takens 9:30-9:55 Self-similarity in Stochastic Peter L. Varkonyi, Budapest University of Bifurcations in the Plane PDEs Technology and Economics, Hungary Peter De Maesschalck, Hasselt University, Wei Wang, Nanjing University, China 9:30-9:55 Testing of a Spacecraft Belgium 10:00-10:25 On the Complete Structure with Non-Smooth 9:30-9:55 Canard Orbits in Planar Slow- Dynamical Behavior for Three Nonlinearities Fast Piecewise-Linear Systems Dimensional Stochastic Competitive Ludovic Renson, J.P. Noel, and G. Soledad Fernandez-Garcia, Mathieu Lotka-VolterraSystems Kerschen, University of Liege, Belgium , Shanghai Normal University, Desroches, and Martin Krupa, INRIA Paris- Jifa Jiang 10:00-10:25 Nonlinear Dynamics and Rocquencourt, France; Antonio E. Teruel, China Bifurcations of Rotor-Stator Contact in University of the Balearic Islands, Spain Rotating Machines 10:00-10:25 Folded Nodes, Canards Nicholas Vlajic, National Institute of and Mixed Mode Oscilations in 3D Standards and Technology, USA; Alan R. Piecewise-Linear Systems Champneys, University of Bristol, United Antonio E. Teruel, University of the Balearic Kingdom; Michael Friswell and Kiran Islands, Spain; Mathieu Desroches, INRIA Vijayan, Swansea University of South Paris-Rocquencourt, France; Enrique Wales, United Kingdom Ponce, Universidad de Sevilla, Spain; Rafel Prohens, University of the Balearic Islands, Spain; Antoni Guillamon, Polytechnic University of Catalonia, Spain; Emilio Freire, Universidad de Sevilla, Spain 2015 SIAM Conference on Applications of Dynamical Systems 77

Thursday, May 21 Thursday, May 21 Thursday, May 21 MS122 Red Sock Award MS6 Announcements Nonlinear Waves in Analysis, Modeling, and Coupled Systems - 11:00 AM-11:15 AM Forecasting in Biomedicine Part I of II Room:Ballroom 1:30 PM-3:30 PM 8:30 AM-10:30 AM Room:Magpie A Room:Primrose B We will discuss how to use biomedical For Part 2 see MS134 IP6 data to reconstruct and forecast state in Traveling waves are special solutions of Brain Control - It’s Not Just different contexts. Specific topics include: partial differential equations posed on infinite (i) model-based forecasting of glucose in domains that have spatially homogeneous for Mad Scientists type 2 diabetics using sparsely collected equilibria. They appear in many applications 11:15 AM-12:00 PM data, (ii) model-based forecasting of sleep- and attract interest not only because they wake cycles, (iii) prediction of recovery of represent coherent structures, but also because Room:Ballroom consciousness in patients with severe brain information about traveling waves helps to Chair: Anthony J. Roberts, University of injury using clinically collected data, and understand complex dynamics of the physical Adelaide, Australia (iv), time series analysis and modeling using system and therefore is of importance for electronic health record data to discover and The brain is an amazing organ - and the general understanding of the underlying forecast drug side effects. The talks will dynamical system - which is responsible phenomenon. In this special session, we focus integrating a diverse set of tools such for a number of important functions bring together researchers who study various as data assimilation, spectral time series including cognition, attention, emotion, aspects of nonlinear waves in coupled analysis and Granger causality with real perception, memory, and motor control. systems of partial differential equations biomedical data. Some brain disorders are hypothesized using analytical and numerical techniques, in to have a dynamical origin; in particular, Organizer: David J. Albers particular addressing the existence, stability, it has been been hypothesized that some Columbia University, USA and speed selection issues. symptoms of Parkinson’s disease are due 1:30-1:55 Time Series Modeling and Organizer: Anna Ghazaryan to pathologically synchronized neural Analysis Using Electronic Health Miami University and University of activity in the motor control region of the Record Data Kansas, USA brain. We have developed a procedure for George Hripcsak, Columbia University, determining an optimal electrical deep brain Organizer: Vahagn Manukian USA stimulus which desynchronizes the activity 2:00-2:25 Predicting Recovery of Miami University, USA of a group of neurons by maximizing the Consciousness in Patients with Brain 8:30-8:55 Nonlinear Waves in a Lyapunov exponent associated with their Injury Lugiato-Lefever Model phase dynamics, work that could lead to an Hans-Peter Frey, Columbia University, Mariana Haragus, Université de Franche- improved “brain control” method for treating USA Comté, France Parkinson’s disease. The use of related control methods for treating other medical 2:30-2:55 Model-Based Glucose 9:00-9:25 The Entry-exit Function and Forecasting for Type 2 Diabetics Geometric Singular Perturbation disorders, including cardiac arrhythmias, will Theory also be discussed. David J. Albers, Columbia University, Peter De Maesschalck, Hasselt University, Jeff Moehlis USA Belgium; Stephen Schecter, North University of California, Santa Barbara, 3:00-3:25 Assimilating Sleep - Putting Carolina State University, USA USA the Model to the Data 9:30-9:55 Oscillons Near Hopf Bruce J. Gluckman, Pennsylvania State Bifurcations of Planar Reaction University, USA Diffusion Equations Kelly Mcquighan, Boston University, USA; Bjorn Sandstede, Brown University, USA Lunch Break 10:00-10:25 Stability of Traveling 12:00 PM-1:30 PM Waves in a Model for a Thin Liquid Film Attendees on their own Flow Vahagn Manukian, Miami University, USA

Coffee Break 10:30 AM-11:00 AM Room:Golden Cliff 78 2015 SIAM Conference on Applications of Dynamical Systems

Thursday, May 21 Thursday, May 21 Thursday, May 21 MS123 MS124 MS125 Spatio-temporal Patterns in Recent Insights into CANCELLED - Data Driven Ecology Controling Flow Structures - Methods for Dynamical 1:30 PM-3:30 PM Part II of II Systems Room:Ballroom I 1:30 PM-3:30 PM 1:30 PM-3:30 PM Many populations and ecosystems exhibit Room:Ballroom II Room:Ballroom III spatial structures, most often generated For Part 1 see MS111 In many applications driven by large-scale by interactions between the organisms Interior flow entities such as fluid interfaces, high-dimensional datasets, there is evidence themselves and their environment. This coherent structures and invariant manifolds of a coarse low-dimensional structure spatial self-organisation may appear as have a profound influence on transport in nonlinearly embedded in the ambient space. patterns in vegetation, in the form of flocks unsteady flows. The ability to control them is Modern nonlinear methods leverage these of birds or schools of fish. The underlying attracting much recent interest, fueled in part coarse geometric structures by constructing driving mechanisms and dynamics are for by emerging biotechnological applications at discrete approximations to operators, such a large part not well-understood. Moreover, the microfluidic level. This minisymposium at the Laplacian, which encode geometric ecological questions about spatio-temporal will cover a range of state-of-the-art information. Applying these methods to data dynamics often generate fundamental approaches to controling flow structures generatedCANCELLED by a dynamical system requires challenges to the mathematical theory. In which are inspired by dynamical systems that they respect the time ordering, which this mini-symposium, various approaches are methods. is the fundamental structure of dynamics. taken to study ecological and mathematical Organizer: Sanjeeva Balasuriya In this special session we discuss recent aspects of the formation of patterns in developments and explore future ideas University of Adelaide, Australia ecological systems. for finding coarse geometric structure in Organizer: Vivi Rottschafer Organizer: Marko Budisic large-scale dynamical datasets with a time- Leiden University, Netherlands University of Wisconsin, Madison, USA ordering, including applications to improve prediction, and uncertainty quantification. Organizer: Arjen Doelman Organizer: Jean-Luc Thiffeault Leiden University, Netherlands University of Wisconsin, Madison, USA Organizer: Dimitrios Giannakis 1:30-1:55 Multi-Objective Optimal Courant Institute of Mathematical 1:30-1:55 Models of Patchy Invasion: Sciences, New York University, USA A Mathematical Toy Or a New Control of Transport and Mixing in Paradigm? Fluids Organizer: Tyrus Berry Sergei Petrovskii, University of Leicester, Kathrin Padberg-Gehle, Dresden Pennsylvania State University, USA United Kingdom University of Technology, Germany; Sina Ober-Blöbaum, University of Paderborn, 2:00-2:25 The Effect of Slow Spatial Germany Processes in a Phytoplankton-Nutrient Model 2:00-2:25 Input-Ouptut Analysis in Lotte Sewalt and Arjen Doelman, Leiden Channel Flows and Implications for University, Netherlands; Antonios Zagaris, Flow Control University of Twente, Netherlands Bassam A. Bamieh, University of California, Santa Barbara, USA 2:30-2:55 Stripe Pattern Selection by Advective RD Systems: Resilience of 2:30-2:55 Correlating Dynamical Banded Vegetation on Slopes Structures with Forcing in 2D Flow Eric Siero and Arjen Doelman, Leiden Nicholas T. Ouellette, Yale University, University, Netherlands; Jens Rademacher, USA University of Bremen, Germany 3:00-3:25 Nematic Liquid Crystal Flow 3:00-3:25 Pattern-formation in a Microfluid: Topological Transitions in Semiarid Vegetation: Using Linda Cummings, New Jersey Institute Bifurcation Theory for Model of Technology, USA; Thomas Anderson, Comparison California Institute of Technology, USA; Sarah Iams, Northwestern University, USA Lou Kondic, New Jersey Institute of Technology, USA 2015 SIAM Conference on Applications of Dynamical Systems 79

Thursday, May 21 Thursday, May 21 Thursday, May 21 MS126 MS127 MS128 Voltage and Calcium Inverse Problems in Network Advances in Computer Dynamics in Single Cells Dynamics - Part II of II Assisted Proof for Infinite and Multicellular Systems 1:30 PM-3:30 PM Dimensional Dynamical 1:30 PM-3:30 PM Room:Wasatch A Systems Room:Magpie B For Part 1 see MS115 1:30 PM-3:30 PM Cardiac cell contraction originates with a Network Dynamics constitutes a rapidly Room:Wasatch B change in membrane potential that leads to expanding field with applications in natural and social science, medicine, engineering, When analyzing global dynamics of infinite a large release of calcium from intracellular dimensional dynamical systems numerical stores and produce contraction. During and beyond. Commonly, mathematical scientists study how a specific network simulation and analytical methods are normal function calcium follows voltage indispensable tools. Starting with the seminal and contraction is uniform. However in model behaves collectively as a function of parameters or inputs. Here, taking a work of Lanford and Eckmann, rigorous disease or extremely fast pacing calcium numerics aims at bridging the apparent gap and voltage coupling can change as well as complementary view, we ask what recorded time series from a network’s units and between what can be computed and what can their respective magnitudes, they can lead to proved rigorously. Mathematically rigorous period doubling bifurcations that in turn can respective correlation and information measures tell us about the units’ local information on global dynamical features is produce complex spatiotemporal patterns and obtained by starting from finite dimensional initiate arrhythmias. In this minisymposium dynamics and their real physical interactions. Such inverse network dynamics are much approximations of a dynamical scaffold we will present experimental results and (fixed points, traveling waves, periodic and theoretical mechanisms that describe some less explored and even less understood. The minisymposium features recent trends, from connecting orbits). This minisymposium of the dynamics between calcium and explores recent advances in rigorous voltage that can lead to cardiac arrhythmias. foundations and applications in time series analysis to models in physics and biology. numerics for topics such as pattern detection Organizer: Flavio Fenton in higher order equations, global dynamics Georgia Institute of Technology, USA Organizer: Michael Rosenblum of parabolic PDEs and infinite dimensional University of Potsdam, Germany maps. Organizer: Yanyan Yi Georgia Institute of Technology, USA Organizer: Marc Timme Organizer: Christian P. Reinhardt Max-Planck-Institute for Dynamics and VU University, Amsterdam, Netherlands 1:30-1:55 Synchronization of Calcium Self-Organization, Germany Sparks and Waves Organizer: Jason Mireles-James Daisuke Sato, University of California, 1:30-1:55 Reconstructing Network Florida Atlantic University, USA Connectivity by Triplet Analysis Davis, USA 1:30-1:55 The Parametrization Method Michael Rosenblum, University of in Infinite Dimensions 2:00-2:25 Nucleation and Dynamics Potsdam, Germany of Spontaneous Ca Waves in Cardiac Christian P. Reinhardt, VU University, Cells 2:00-2:25 Dynamic Information Amsterdam, Netherlands; Jason Mireles- Yohannes Shiferaw, California State Routing in Complex Networks James, Florida Atlantic University, USA Christoph Kirst, Rockefeller University, University, Northridge, USA 2:00-2:25 Rigorous Numerics for Some USA 2:30-2:55 Effects of Implementing Pattern Formation Problems Contraction to Calcium-Voltage 2:30-2:55 Unraveling Network Jan Bouwe Van Den Berg, VU University, Models Topology from Derivative-Variable Amsterdam, Netherlands Correlations Yanyan Ji, Georgia Insitute of Technology, 2:30-2:55 Rigorous Numerics for Zoran Levnajic, Laboratory of Data USA and Jagiellonian University, Poland; Symbolic Dynamics and Topological Technologies, Slovenia Flavio M. Fenton, Georgia Institute of Entropy Bounds Technology, USA; Richard Gray, U.S. 3:00-3:25 From Neural Dynamics to Sarah Day, College of William & Mary, Food and Drug Administration, USA Network Properties and Cognitive USA; Rafael Frongillo, University of 3:00-3:25 Complex Dynamic Function California, Berkeley, USA Daniel Maruyama, Nicollette Ognjanovski, Patterns of Voltage and Calcium in 3:00-3:25 Orbital Stability Sara Aton, and Michal Zochowski, Mammalian Hearts Investigations for Travelling Waves in University of Michigan, USA Ilija Uzelac and Flavio M. Fenton, Georgia a Nonlinearly Supported Beam Institute of Technology, USA Michael Plum, Karlsruhe University, Germany 80 2015 SIAM Conference on Applications of Dynamical Systems

Thursday, May 21 Thursday, May 21 2:30-2:55 Mixed-Mode Bursting Oscillations (MMBOs): Slow Passage MS129 MS130 Through a Spike-adding Canard Explosion Complex Collective Recent Advances on Mathieu Desroches, INRIA Paris- Dynamics of Oscillator Multiple Timescale Rocquencourt, France; Tasso J. Kaper, Networks - Part II of II Dynamics - Part II of II Boston University, USA; Martin Krupa, INRIA Paris-Rocquencourt, France 1:30 PM-3:00 PM 1:30 PM-3:30 PM 3:00-3:25 Averaging, Folded Room:Maybird Room:Superior A Singularities and Torus Canards in a Coupled Neuron Model For Part 1 see MS117 For Part 1 see MS118 Kerry-Lyn Roberts, University of Sydney, Considerable progress has recently been made Multiple timescales are ubiquitous in models Australia; , in understanding the collective dynamics of of real-world phenomena such as neuron Jonathan E. Rubin University of Pittsburgh, USA; Martin large oscillator networks. New analytical firing, laser dynamics, and climatic rhythms. Wechselberger, University of Sydney, tools have been created and extended in Differential equations involving variables Australia their applicability, and novel effects have evolving on distinct timescales yield rich and been demonstrated not only theoretically and notoriously hard mathematical questions. numerically, but also experimentally. Results This two-part minisymposium presents in this field have broad application to both recent results on singularly perturbed ODEs, physical and biological systems. Part one of which is the most amenable paradigm for this symposium will report recent general analysis of multiple timescale phenomena. mean field results involving chimera states, We will give a panorama of this topic, from assortative networks, and generalizations of theoretical work on planar canard problems, the classic Kuramoto model. Part two will in both smooth and non-smooth vector fields focus on networks of neuronal oscillators, (Part I), to more application-driven studies their relationship to field models, and the of complex oscillations with at least three dynamical consequences of connectivity. variables and two or more timescales (Part II). Organizer: Paul So George Mason University, USA Organizer: Mathieu Desroches INRIA Paris-Rocquencourt, France Organizer: Arkady Pikovsky University of Potsdam, Germany Organizer: Vivien Kirk University of Auckland, New Zealand Organizer: Ernest Barreto George Mason University, USA Organizer: Jonathan E. Rubin University of Pittsburgh, USA 1:30-1:55 Neural Field Models Which Include Gap Junctions 1:30-1:55 Three Timescale Carlo R. Laing, Massey University, New Phenomena in Coupled Morris-Lecar Zealand Equations Pingyu Nan, University of Auckland, New 2:00-2:25 From Ensembles of Pulse- Zealand; Yangyang Wang, University of Coupled Oscillators to Firing-Rate Pittsburgh, USA; Vivien Kirk, University Models of Auckland, New Zealand; Jonathan E. Diego Pazó, Instituto de Física de Cantabria Rubin, University of Pittsburgh, USA (IFCA), Spain; Ernest Montbrio, Universitat Pompeu Fabra, Spain; Alex Roxin, Centre 2:00-2:25 An Organizing Center for de Recerca Matemàtica, Spain Spatiotemporal Bursting Alessio Franci, University of Cambridge, 2:30-2:55 Suppressing Complex United Kingdom; Guillaume Drion, Collective Behavior in a Network of Brandeis University, USA; Rodolphe Theta Neurons by Synaptic Diversity Sepulchre, University of Cambridge, Lucas Lin, Thomas Jefferson High School United Kingdom of Science and Techonology, USA; Ernest Barreto and Paul So, George Mason University, USA

continued in next column 2015 SIAM Conference on Applications of Dynamical Systems 81

Thursday, May 21 Thursday, May 21 Thursday, May 21 MS131 MS132 MS133 Uncertainty Propogation in Stochastic Dynamics Engineering Applications High Dimensional Systems and Their Applications - of Non-smooth Dynamics - 1:30 PM-3:30 PM Part II of II Part II of II Room:Superior B 1:30 PM-3:00 PM 1:30 PM-3:30 PM Uncertainty can be found everywhere Room:White Pine Room:Primrose A in real control systems, from the sensor For Part 1 see MS120 For Part 1 see MS121 readings to the dynamics themselves. Given Stochastic dynamical concepts are crucial Friction and impact are challenging research incomplete knowledge one must have a in modelling the dynamical behavior of areas of engineering. These phenomena means of estimating the likelihood of a dynamical systems under uncertainty. are commonly described by empirical given event, such as the toppling over of There are some theory results of the models, such as the coefficient of restitution a robotic walker. In terms of computation, stochastic dynamics such as the stochastic or various friction models, including the this is a substantially greater challenge attractors, invariant manifolds, invariant Coulomb-Amontons’ law. Modelling than deterministic prediction. Computing measures. However, the theory is restricted contact mechanics from first principles is likelihood boils down to computing the on some conditions. Applied science and almost impossible, each model needs some advection of a probability density. This is engineering requires more stochastic parameter fitting. Even when a model is typically an infinite dimensional inverse dynamical techniques. The objective available, one might not be able to solve it problem. In this series of talks we present of this minisymposium is to bring the due to various mathematical singularities, a range of approaches for attacking this bridge between the new theory methods where there is no unique prediction. problem numerically. and approaches to stochastic dynamics in This minisymposium shows a number of Organizer: Henry O. Jacobs applications. applications where the ‘rough’ terrain of Imperial College London, United Organizer: Xiaopeng Chen non-smooth dynamics must be carefully navigated. Attempts will be also made to Kingdom Peking University, China resolve singularities and identify contact Organizer: Ram Vasudevan Organizer: Jinqiao Duan force models. University of Michigan, USA Illinois Institute of Technology, USA Organizer: Robert Szalai 1:30-1:55 Optimal Control Design 1:30-1:55 How to Quantify Non- University of Bristol, United Kingdom and Value Function Estimation for Gaussian Stochastic Dynamics? 1:30-1:55 Contact and Friction Within Nonlinear Dynamical Systems , Illinois Institute of Jinqiao Duan Geometrically Exact Shell Theory - Milan Korda, École Polytechnique Fédérale Technology, USA de Lausanne, Switzerland Modeling Microslip and Dissipation in 2:00-2:25 Random Dynamical Structural Systems 2:00-2:25 Transfer Operator Methods Systems for Non-Densely Defined D Dane Quinn, University of Akron, USA for Stability Analysis and Control Evolution Equations Umesh Vaidya, Iowa State University, USA 2:00-2:25 A New Semi-Analytical Alexandra Neamtu, Friedrich Schiller Algorithm for Two-Dimensional 2:30-2:55 Unitary Representations of Universität Jena, Germany Coulomb Frictional System Diffeomorphisms: Halfway Between 2:30-2:55 Stochastic Center Manifolds Xiaosun Wang, Wuhan University, China; Koopmanism and Transfer Operator Without Gap Conditions Jim Barber, University of Michigan, USA Theory Xiaopeng Chen, Peking University, China Henry O. Jacobs, Imperial College London, 2:30-2:55 Lessons Learnt from the United Kingdom Two-Ball Bounce Problem Yani Berdeni, University of Bristol, United 3:00-3:25 Numerical Advection Kingdom of Probability Densities for High Dimensional Systems 3:00-3:25 Predicting Conditions for Ram Vasudevan, University of Michigan, Self-sustained Vibration in Drillstrings USA Tore Butlin, University of Cambridge, United Kingdom 82 2015 SIAM Conference on Applications of Dynamical Systems

Thursday, May 21 Thursday, May 21 MS134 Closing Remarks Nonlinear Waves in 4:00 PM-4:15 PM Coupled Systems - Room:Ballroom Part II of II 1:30 PM-3:30 PM Room:Primrose B IP7 For Part 1 see MS122 The Robotic Scientist: Traveling waves are special solutions Distilling Natural Laws from of partial differential equations posed Raw Data, from Robotics to on infinite domains that have spatially homogeneous equilibria. They appear Biology and Physics in many applications and attract interest 4:15 PM-5:00 PM not only because they represent coherent structures, but also because information Room:Ballroom about traveling waves helps to understand Chair: Timothy Sauer, George Mason complex dynamics of the physical system University, USA and therefore is of importance for the general understanding of the underlying Can machines discover scientific laws phenomenon. In this special session, we automatically? Despite the prevalence of bring together researchers who study various computing power, the process of finding aspects of nonlinear waves in coupled natural laws and their corresponding systems of partial differential equations equations has resisted automation. This using analytical and numerical techniques, in talk will outline a series of recent research particular addressing the existence, stability, projects, starting with self-reflecting robotic and speed selection issues. systems, and ending with machines that can formulate hypotheses, design experiments, Organizer: Anna Ghazaryan and interpret the results, to discover new Miami University and University of scientific laws. We will see examples from Kansas, USA psychology to cosmology, from classical Organizer: Vahagn Manukian physics to modern physics, from big science Miami University, USA to small science. 1:30-1:55 An Overview of Evans Hod Lipson Function Computation Cornell University, USA Jeffrey Humpherys, Brigham Young University, USA 2:00-2:25 Invasion Fronts in Systems of Reaction Diffusion Equations Matt Holzer, George Mason University, USA 2:30-2:55 Orbital Stability of Waves Traveling Along Vortex Filaments Stéphane Lafortune, College of Charleston, USA 3:00-3:25 Stability of Combustion Fronts in Hydraulically Resistant Porous Media Anna Ghazaryan, Miami University, USA

Coffee Break 3:30 PM-4:00 PM Room:Golden Cliff 2015 SIAM Conference on Applications of Dynamical Systems 83 84 2015 SIAM Conference on Applications of Dynamical Systems

2017

21-25, 7

Save the Date! 2017 SIAM Conference on Applications of Dynamical Systems May 21-25, 2017 Snowbird Ski and Summer Resort Snowbird, Utah, USA 2015 SIAM Conference on Applications of Dynamical Systems 85

Save the Dates! 86 2015 SIAM Conference on Applications of Dynamical Systems

Notes 2015 SIAM Conference on Applications of Dynamical Systems 87

DS15 Abstracts

2015

Abstracts are printed as submitted by the authors. 88 DS15 Abstracts

IP1 ”Long-time asymptotics of the filtering distribution for Advances on the Control of Nonlinear Network Dy- partially observed chaotic deterministic dynamical sys- namics tems” (http://arxiv.org/abs/1411.6510); see also the pa- per K.J.H. Law, A. Shukla and A.M. Stuart, ”Analysis An increasing number of complex systems are now mod- of the 3DVAR filter for the partially observed Lorenz ’63 eled as networks of coupled dynamical entities. Nonlinear- model,’” Discrete and Continuous Dynamical Systems A, ity and high-dimensionality are hallmarks of the dynam- 34(2014), and the book K.J.H. Law, A.M.Stuart and K. ics of such networks but have generally been regarded as Zygalalkis, ”Data Assimilation: A Mathematical Introduc- obstacles to control. In this talk, I will discuss recent ad- tion” (in preparation, 2015) for further background refer- vances on mathematical and computational approaches to ences. control high-dimensional nonlinear network dynamics un- der general constraints on the admissible interventions. I Andrew Stuart will present applications to the stabilization of power grids, Mathematics Institute, identification of new therapeutic targets, mitigation of ex- University of Warwick tinctions in food webs, and control of systemic failures in [email protected] socio-economic systems. These examples will illustrate the potential and limitations of existing methods to address a IP4 broad class of problems, ranging from cascade control and transient stability to network reprogramming in general. Fields of Dreams: Modeling and Analysis of Large Scale Activity in the Brain Adilson E. Motter Northwestern University With the advent of optogenetics and the ability to record [email protected] large numbers of neurons with high temporal resolution, there is now a great deal of interest in both the tempo- ral and spatial activity of neurons in the brain. In this IP2 talk, I will discuss a number of old and new developments in the study of these nonlinear integro-differential equa- Mathematics of Crime tions and how they apply to some new biological find- There is an extensive applied mathematics literature devel- ings. Topics that I will discuss include the role of noise on oped for problems in the biological and physical sciences. spatio-temporal activity, the interaction between extrinsic Our understanding of social science problems from a math- and intrinsic activity, interactions between multiple spatial ematical standpoint is less developed, but also presents networks, and finally some recent applications of Filippov some very interesting problems, especially for young re- theory to discontinuous neural field models. searchers. This lecture uses crime as a case study for using Bard Ermentrout applied mathematical techniques in a social science appli- University of Pittsburgh cation and covers a variety of mathematical methods that Department of Mathematics are applicable to such problems. We will review recent [email protected] work on agent based models, methods in linear and non- linear partial differential equations, variational methods for inverse problems and statistical point process models. IP5 From an application standpoint we will look at problems Cooperation, Cheating, and Collapse in Biological in residential burglaries and gang crimes. Examples will Populations consider both ”bottom up’ and ”top down’ approaches to understanding the mathematics of crime, and how the two Natural populations can suffer catastrophic collapse in re- approaches could converge to a unifying theory. sponse to small changes in environmental conditions as a result of a bifurcation in the dynamics of the system. Andrea L. Bertozzi We have used laboratory microbial ecosystems to directly UCLA Department of Mathematics measure theoretically proposed early warning signals of [email protected] impending population collapse based on critical slowing down. Our experimental yeast populations cooperatively break down sugar, meaning that below a critical size the IP3 population cannot sustain itself. The cooperative nature of Filtering Partially Observed Chaotic Deterministic yeast growth on sucrose makes the population susceptible Dynamical Systems to ”cheater” cells, which do not contribute to the public good and reduce the resilience of the population. This talk is concerned with determining the state of a chaotic dynamical system, for which the initial condition Jeff Gore is only known probabilisticlly, given partial and noisy ob- Massachusetts Institute of Technology servations. In particular it is of interest to study this prob- [email protected] lem in the limit of a large number of such observations, over a long time interval. A key question is to deter- mine which observations are sufficient in order to accu- IP6 rately recover the signal, and thereby overcome the lack Brain Control - It’s Not Just for Mad Scientists of predictability caused by sensitive dependence on ini- tial conditions. A canonical application is the develop- The brain is an amazing organ - and dynamical system - ment of probabilistic weather forecasts. In order to study which is responsible for a number of important functions in- this problem concretely, we will focus on a wide class of cluding cognition, attention, emotion, perception, memory, dissipative differential equations with quadratic energy- and motor control. Some brain disorders are hypothesized conserving nonlinearity, including the Navier-Stokes equa- to have a dynamical origin; in particular, it has been been tion on a two dimensional torus. The work presented is hypothesized that some symptoms of Parkinson’s disease contained in the paper D. Sanz-Alonso and A.M.Stuart, are due to pathologically synchronized neural activity in DS15 Abstracts 89

the motor control region of the brain. We have developed a index form a finite dimensional manifold. Furthermore, procedure for determining an optimal electrical deep brain for a large class of nonlinearities f we can count index 1 stimulus which desynchronizes the activity of a group of solutions. This allows us to define Morse-Floer homology neurons by maximizing the Lyapunov exponent associated groups, which are invariant with respect to continuation of with their phase dynamics, work that could lead to an im- f. proved ”brain control” method for treating Parkinson’s dis- ease. The use of related control methods for treating other Berry Bakker, Jan Bouwe Van Den Berg, Robert van Der medical disorders, including cardiac arrhythmias, will also Vorst be discussed. VU University Amsterdam [email protected], [email protected], vd- Jeff Moehlis [email protected] Dept. of Mechanical Engineering University of California – Santa Barbara [email protected] CP1 Reaction-Diffusion Equations with Spatially Dis- tributed Hysteresis in Higher Spatial Dimensions IP7 The Robotic Scientist: Distilling Natural Laws Many chemical and biological processes are modelled by from Raw Data, from Robotics to Biology and reaction-diffusion equations with a nonlinearity involving Physics hysteresis. In such problems each spatial point can be in one of two configurations and the configuration changes in Can machines discover scientific laws automatically? De- time via a hysteresis law. Points in different configurations spite the prevalence of computing power, the process of segregate the domain into several subdomains and switch- finding natural laws and their corresponding equations has ing implies that these subdomains are separated by free resisted automation. This talk will outline a series of re- boundaries. We will discuss how the hysteresis gives rise cent research projects, starting with self-reflecting robotic to a novel type of free boundary evolution. systems, and ending with machines that can formulate hy- potheses, design experiments, and interpret the results, to Mark J. Curran discover new scientific laws. We will see examples from Free University of Berlin psychology to cosmology, from classical physics to modern [email protected] physics, from big science to small science. Hod Lipson CP1 Cornell University, USA Existence of Periodic Solutions of the FitzHugh- [email protected] Nagumo Equations for An Explicit Range of the Small Parameter

SP1 We consider the FitzHugh-Nagumo system describing Juergen Moser Lecture - Dynamics and Data nerve impulse propagation in an axon. With aid of computer-assisted rigorous computations we are able to This lecture highlights interdisciplinary interactions of dy- show the existence of the periodic pulse for an explicit namical systems theory. Experimental data and computer range of singular perturbation parameter  ∈ (0,0]. Our simulation have inspired mathematical discoveries, while right bound 0 is large enough to be reached by validated resulting theory has made successful predictions and cre- continuation methods designed for ODEs without time ated new scientific perspectives. Nonlinear dynamics has scale separation. unified diverse fields of science and revealed deep mathe- matical phenomena. Examples involving Aleksander Czechowski, Piotr Zgliczy´nski • Jagiellonian University, Poland One dimensional maps [email protected], [email protected] • Numerical bifurcation analysis • Multiple time scales CP1 • Bursting and MMOs in neuroscience and chemistry Spatio-Temporal Dynamics of Heterogeneous Ex- • Locomotion citable Media are described, along with emerging areas having public im- The propagation of electrical waves in biological tissue or pact. concentration waves in chemical reactions are examples for complex dynamics in excitable media. Already sim- John Guckenheimer ple homogeneous reaction-diffusion systems reveal a rich Cornell University diversity of dynamical patterns, including spiral waves [email protected] and spatio-temporal chaos. Here we consider excitable media including heterogeneities and study their (tran- CP1 sient) dynamics in numerical simulations employing (co- variant) Lypaunov Vectors, (linear) mode decompositions, Morse-Floer Homology for Travelling Waves in and diffusion-mapped delay coordinates. Reaction-Diffusion Equations Thomas Lilienkamp This talk is about heteroclinic solutions u of Max Planck Institute for Dynamics and Self-Organization 2 Biomedical Physics Research Group ∂t u − c∂tu +Δxu + f(u)=0. [email protected] For suitable (nonlocal) perturbations of this equation solu- tions can be assigned an index, and solutions with a fixed Ulrich Parlitz, Stefan Luther 90 DS15 Abstracts

Max Planck Institute for Dynamics and Self-Organization Component System (TCS) model of morphogen (m) and Research Group Biomedical Physics modulator (M) that interact and spatially alter the bio- [email protected], [email protected] chemical properties of each other. We identified a num- ber of network motifs that confer scaling and robustness of morphogen patterning including bilateral repression and CP1 others. Low Dimensional Models of Diffusion and Reaction in Stratified Micro Flows Md. Shahriar Karim Purdue University We develop a low dimensional model of simultaneous in- [email protected] terphase mass transfer and reaction in two-phase stratified flows through microchannels. Here, diffusion quickly equi- Hans G. Othmer librates the distribution of species in the lateral direction. University of Minnesota This singularly perturbed dynamical system has a slow Department of Mathematics invariant manifold, which is parameterized by a suitably [email protected] weighted laterally averaged concentration. The Lyapunov- Schmidt reduction of bifurcation theory is used to compute David Umulis this manifold and derive reduced order models for arbitrary Dept. of Ag. and Biological Engineering, Purdue reaction kinetics. University Jason R. Picardo, Subramaniam Pushpavanam West Lafayette, IN-47904, USA Department of Chemical Engineering [email protected] Indian Institute of Technology Madras [email protected], [email protected] CP2 Solitary Waves in the Excitable Discrete Burridge- CP1 Knopoff Model Defect Solutions in Reaction-Diffusion Equations The Burridge-Knopoff model describes the dynamics of an In this talk, I will discuss the effect a heterogeneity can elastic chain of blocks pulled over a surface. This model have on the pattern formation process for two different accounts for nonlinear friction phenomena and displays ex- types of reaction-diffusion equations. These heterogeneities citability when the velocity-dependent friction force is non- for example arise in models where a particular species is monotone. We introduce a simplified piecewise linear fric- only produced in a particular part of the domain of interest. tion law (reminiscent of the McKean nonlinearity in spiking I will mainly focus on the pinning of solutions near and neuron models) which allows us to analyze the existence away from the heterogeneity. of large amplitude solitary waves. Propagation failure is shown to occur for weakly coupled oscillators. Peter van Heijster Mathematical Sciences School Jose Eduardo Morales Morales Queensland University of Technology INRIA Rhone Alpes [email protected] [email protected]

Guillaume James, Arnaud Tonnelier CP2 INRIA - Rhˆone Alpes Generalized Behavior of the Two-phase System in [email protected], [email protected] (1+1) D

The two-phase model is well known for its applications in CP2 gel-dynamics. A network made of an extracellular poly- Aspects and Applications of Generalized Synchro- meric substance (EPS) is immersed in a fluid solvent. The nization network provides a layer of protection for bacterial growth. We find a general reduction in the two-phase system for an Different concepts of generalized synchronization of cou- arbitrary growth in (1+1) D to a system of a single vari- pled (chaotic) dynamical systems and corresponding time able. This system emits several solutions. The first two series analysis methods are revisited and compared. Fur- solutions show that in the presence of logistic growth in thermore, we address the relation to snapshot attractors a frictionless environment, osmotic pressure has a negli- as well as potential applications of generalized synchro- gible effect. The third solutions shows that the inviscid nization for state estimation and data assimilation. For all two-phase system emits shocks and rarefactions. topics representative examples will be given to illustrate the main statements. David A. Ekrut, Nicholas Cogan Florida State University Ulrich Parlitz [email protected], [email protected] Max Planck Institute for Dynamics and Self-Organization Research Group Biomedical Physics [email protected] CP2 Scaling and Robustness of Two Component Mor- phogen Patterning Systems CP2 Discrete Synchronization of Massively Connected Embryonic development requires highly reproducible Systems Using Hierarchical Couplings mechanisms of pattern formation so that cell fate is as- signed at the right time and location. To identify the We study the synchronization of massively connected net- mechanisms of pattern regulation, we developed a Two works of which interactions come from successive hierar- DS15 Abstracts 91

chical couplings. Motivations of this work come from the [email protected] growing necessity of understanding properties of complex systems that often exhibit a hierarchical structure. Start- ing with a set of 2n coupled maps, we obtain synchroniza- CP3 tion results for infinitely many, i.e for a Cantor set of maps. Analysis of Connected Vehicle Networks with Non- We also prove synchronization happens when the network trivial Connectivity, a Modal Decomposition Ap- is still massively connected but with an infinite number of proach broken links inside the hierarchical structure. Connected vehicles that communicate via wireless vehicle- Camille Poignard to-vehicle communication are gaining increasing attention Doctor due to their potential in improving traffic safety, mobil- [email protected] ity, and efficiency. As connected vehicle systems become more complex, the analysis of the arising networked dy- namical systems becomes more challenging. We present a CP2 novel method to analyze the network modes by expansion around a network of simple connectivity, and demonstrate Nonlinear Dynamics of Two-Colored Filaments that unstable traffic flow can be stabilized using long-range interactions. Propagation of light filaments is a highly nonlinear process that results from light-matter interactions. It is impor- Sergei S. Avedisov tant area in nonlinear optics with much ongoing theoreti- University of Michigan, Ann Arbor cal and experimental research efforts. While there has been [email protected] much progress in both fronts, there remain many challenges to produce long-lived filaments. Modeling requires good Gabor Orosz understanding of light matter interactions with a particu- University of Michigan, Ann Arbor lar objective of determining conditions that limits spatio- Department of Mechanical Engineering temporal instabilities thus producing quasi-stable dynam- [email protected] ics. While typical studies concentrate on optical filaments at a single frequency, mostly in the infrared (IR) and the ul- traviolet (UV) wavelengths, under suitable conditions non- CP3 linear wave-mixing can lead to multicolored filaments. In Simulating the Dynamics of College Drinking this talk I will present new results that consider the co- existence of UV/IR filaments under a variety of spatial Heavy episodic or binge drinking is among the most diffi- configurations cult public health challenges on college campuses. Integrat- ing peer influence models from public health and identity Alexey Sukhinin, Alejandro Aceves verification from social psychology as mechanisms that in- Southern Methodist University fluence drinking behavior, we develop an agent-based simu- [email protected], [email protected] lation to examine the dynamics of drinking events, as stu- dents group together and interact. We also consider the conditions necessary for widely-used social norms interven- CP3 tions to be effective.

Heterogeneities in Temporal Networks Emerging Ben G. Fitzpatrick, Jason Martinez, Elizabeth Polidan from Adaptive Social Interactions Tempest Technologies fi[email protected], martinez@tempest- Recent studies on social empirical data have revealed het- tech.com, [email protected] erogeneities in human dynamics, which are signs of the distinctive mechanism underlying the dynamical behaviors of societies. It is known that human activity is bursty, CP3 and the social interactions have scale-free structures. To Integrating Hydrological and Waterborne Disease facilitate unified understanding of social dynamics and net- Network Models works, we propose a model of adaptive temporal networks. Under suitable conditions, this model exhibits heteroge- Mechanistic drivers of the seasonal patterns of cholera in neous temporal and structural behaviors even from a com- Bangladesh remain poorly understood. A community net- pletely homogenous initial condition. work model for cholera dynamics is developed. A hydro- logical model for the Ganges-Brahmaputra-Meghna river Takaaki Aoki basin is integrated into the disease network model to ac- Faculty of Education count for seasonality of surface water connectivity and con- Kagawa university tamination. We demonstrate that the integrated model can [email protected] contribute to the understanding of disease dynamics and potentially to the development of disease forecasting tools. Luis Rocha Department of Public Health Sciences Karly Jacobsen Karolinska Institutet, Solna, Sweden Mathematical Biosciences Institute [email protected] The Ohio State University [email protected] Thilo Gross Department of Engineering Mathematics and Bristol Michael Kelly Centre for The Ohio State University University of Bristol, Bristol, UK [email protected] 92 DS15 Abstracts

Faisal Hossain adaptive reduced order models for improved observation University of Washington and control. We present some numerical results for the [email protected] case of Navier Stokes and Boussinesq equations.

Joseph H. Tien Piyush Grover Ohio State University Mitsubishi Electric Research Laboratories Department of Mathematics [email protected] [email protected] Boris Kramer Virginia Tech CP3 [email protected] Phase Response Properties of Collective Rhythms in Networks of Coupled Dynamical Systems Petros Boufounos, Mouhacine Benosman Mitsubishi Electric Research Laboratories Phase response property of a network of diffusively cou- [email protected], [email protected] pled dynamical units undergoing collective oscillations is studied. Each unit can possess arbitrary local dynamics as long as the whole coupled system exhibits stable limit- CP4 cycle oscillations. The phase response property of the sys- Bifold Visualization of Dynamic Networks tem can be decomposed into Laplacian eigenmodes of the coupling network, which reveals how each individual mode We consider binary datasets arising from bipartite data, contributes to the total phase response. Phase synchro- where the data describes the relationships between two nization of simple dynamical networks is analyzed as an types of entities (such as a user “liking’ a certain movie). example. Comparing the binary patterns between entities provides a dissimilarity measure which allows projecting that data Hiroya Nakao in a Euclidean representation. We apply our algorithm Graduate School of Information Science and Engineering, to datasets of US senators and their voting records. By Tokyo Institute of Technology simultaneously representing intergroup and intragroup re- [email protected] lationships, significant additional insight is provided by the visualization. Sho Yasui Graduate School of Information Science and Engineering Yazhen Jiang, Joseph Skufca, Jie Sun Tokyo Institute of Technology Clarkson University [email protected] [email protected], [email protected], [email protected]

CP4 Prediction in Projection CP4 An Algorithmic Approach to Computing Lattice Full and accurate reconstruction of dynamics from time- Structures of Attractors series data—e.g., via delay-coordinate embedding—is a real challenge in practice. For the purposes of forecast- We describe the lifting of sublattices of attractors, which ing, however, reconstructions that do not satisfy the di- are computationally less accessible, to lattices of forward mension conditions of the embedding theorems can still invariant sets and attracting neighborhoods, which are be quite useful. Despite the lack of topological conjugacy, computationally accessible. We provide necessary and suf- near-neighbor forecast methods working in these reduced- ficient conditions for such a lift to exist along with algo- order spaces are as (or more) effective than in complete rithms to check whether such conditions are met or not and embeddings. We demonstrate this using both synthetic to construct the lift if met. We illustrate the algorithms and experimental time series data. with some examples.

Joshua Garland Dinesh Kasti University of Colorado at Boulder Florida Atlantic University [email protected] [email protected]

Elizabeth Bradley William D. Kalies University of Colorado Florida Atlantic University Department of Computer Science Department of Mathematical Sciences [email protected] [email protected]

Robertus Vandervorst CP4 Vrije Universiteit Amsterdam Sparse Sensing Based Detection of Dynamical Phe- [email protected] nomena and Flow Transitions

Reduced order models for fluid dynamics are often sensitive CP4 to changes in flow topology and require some information Expanded Mixed Finite Element Method for Gen- about the dynamical regime of operation. Using sparse eralized Forchheimer Flows sensing and reconstruction techniques, we present a frame- work to detect dynamical phenomena such as bifurcations We study the expanded mixed finite element method ap- and changes in flow topology in a variety of thermo-fluid plied to the Forchheimer fluid flow in porous media. The dynamical systems. This framework can be combined with bounds for the solutions are established. Utilizing the spe- DS15 Abstracts 93

cial properties of Forchheimer equation and boundedness of [email protected] solutions we prove the optimal error estimates in L2-norm for solution. The error bounds are established for the so- lution and divergence of the vector variable in Lebesgue CP5 norms and Sobolev norms. A numerical example using Mathematical Models of Seasonally Migrating Pop- the lowest order Raviart-Thomas (RT0) mixed element are ulations provided agreement with our theoretical analysis. Predator-prey systems that allow for one or more species Thinh T. Kieu to undergo mass migration open up a range of new possi- University of North Georgia bilities from a dynamical point of view. We consider two [email protected] different approaches to modelling problems of this type, namely, ordinary and partial differential equations. In both cases the inclusion of time switches is key to understand- Akif Ibraguimov ing their behaviour and allows us to consider the effects Department of Mathematics and Statistics. of timing mismatches brought about by changing climatic Texas Tech University conditions. [email protected] John G. Donohue National University of Ireland, Galway CP4 [email protected] A Method for Identification of Spatially-Varying PetriT.Piiroinen Parameters Despite Missing Data with Applica- School of Mathematics, Statistics and Applied tion to Remote SensingA Method for Identification Mathematics of Spatially-Varying Parameters Despite Missing National University of Ireland, Galway Data with Application to Remote Sensing [email protected] Remote sensing data allows for ecological inferences over large-scale oceanic regions. Proposed models require pa- CP5 rameter tuning to match data observations, including syn- A Model for Mountain Pine Beetle Outbreaks in chronization and filtering methods. A major hindrance in An Age Structured Forest: Approximating Sever- applying synchronization methods to remote sensing data ity and Outbreak-Recovery Cycle Period is the frequency with which clouds hide parts of a satellite image. A synchronization method is discussed to infer un- We develop a system of difference equations to model known model parameters and states, despite hidden data. (temperature-driven) mountain pine beetle infestation in We treat a PDE as a temporally-varying network to prove an age-structured forest. Equilibrium stability analysis the method. indicates the existence of periodic outbreaks that inten- sify as growth rates increase. Analytical methods are de- Sean Kramer, Erik Bollt vised to predict outbreak severity, duration, and frequency. Clarkson University The model predicts cycle periods that fall within observed [email protected], [email protected] outbreak period ranges. To assess future beetle impact on forests, we predict severity of outbreaks in the face of changing climate. CP5 Jacob P. Duncan, James Powell, Luis Gordillo A Mathematical Model for the Sexual Selection of Utah State University Extravagant and Costly Mating Displays [email protected], [email protected], [email protected] The evolution of extravagant and costly ornaments on an- imals has intrigued biologists and mathematicians since Joseph Eason Darwin suggested that female preference for exaggerated University of Utah courtship displays drives the sexual selection of these or- [email protected] naments. We propose a minimal mathematical model that incorporates two components of ornament evolution: an CP5 intrinsic cost and/or benefit of ornamentation to an indi- vidual, and a social benefit of relatively large ornaments Host-Mediated Responses on the Dynamics of within a population. Using bifurcation analysis and per- Host-Parasite Interaction turbation theory, we show that on an evolutionary time scale, identically healthy animals will split into two niches, The regulation of helminth populations within hosts de- one with large ornaments and one with small. This result pends on host age, immunity and density-dependent con- may explain why ecologists have observed bimodal distri- straints. Laboratory infections reveal that rabbit immu- butions of ornament size in several species. nity limits worm growth and reduces fecundity. Continu- ous natural exposure of rabbits to worms generates a neg- ative relationship between rabbit age and worm fecundity. Sara Clifton Using an age-structured population model we show how Northwestern University, USA these regulatory factors stabilize the dynamical behaviour [email protected] of between-host transmission via egg shedding through maintaining a self-sustained oscillation in rabbit genera- DanielAbrams,DanielThomas tions. Northwestern University [email protected], Suma Ghosh, Matthew Ferrari 94 DS15 Abstracts

The Pennsylvania State University Fathi Bribesh [email protected], [email protected] Department of Mathematics Zawia University, Zawia, Libya [email protected] CP5 Geometric Dissection of a Model for the Dynamics Uwe Thiele of Bipolar Disorders Institute of Theoretical Physics University of Muenster We study a model for the dynamics of bipolar disorders [email protected] developed by A. Goldbeter. The model is four-dimensional and not in the standard form of slow-fast systems. The geometric analysis of the model is based on identifying and CP6 using hierarchies of local approximations based on various Escape from Potential Wells in Multi-Degree of - hidden – forms of time scale separation. A central tool Freedom Systems: Phase Space Geometry and Par- in the analysis is the blow-up method which allows the tial Control identification of a complicated singular cycle. Predicting the escape from a potential energy well is a uni- Ilona Kosiuk versal exercise, governing myriad engineering and natural MPI MiS systems, e.g., buckling phenomena, ship capsize, and hu- Inselstrasse 22, 04103 Leipzig Germany man balance. For such systems, tube dynamics provides [email protected] the phase space criteria for escape. We consider a control problem where the goal is to avoid escape in the presence Ekaterina Kutafina of large disturbances which are greater in magnitude than AGH University of Science and Technology the controls by implementing a safe-set-sculpting algorithm Cracow, Poland which explicitly incorporates tube dynamics. ekaterina.kutafi[email protected] Shibabrat Naik Peter Szmolyan Engineering Science and Mechanics Vienna University of Technology Virginia Tech Vienna, Austria [email protected] [email protected] Shane D. Ross Virginia Tech CP6 Engineering Science and Mechanics Continuation of Bifurcations in Physical Experi- [email protected] ments

A good mathematical model for a specific physical sys- CP6 tem can be hard to create. Fortunately, the low cost and Periodic Social Niche Construction easy availability of high-speed electronics now enables real- time integration of numerical methods and physical ex- Social niche construction describes the creation of social periments. This opens up a wide range of new possibil- networks and institutions that influence individual fitness. ities in experimental nonlinear dynamics. Here we outline Niche construction involves multiple timescales, including the current state-of-the-art in control-based continuation, a the relatively short time required to build a niche, and the method for tracking the solutions and bifurcations directly longer time required to learn how to build a niche. We in a physical experiment. explore a number of learning rules for niche construction in relation to competition between constructing species or David A. Barton agents, in particular the dynamics of institutional switch- University of Bristol, U.K. ing, as the system undergoes a Hopf-bifurcation. Hysteresis [email protected] in key competition parameters provides evidence of top- down causal memory from the institutions, leading to in- creased resistance to change between states. This is due to CP6 the different stability criteria for a periodic solution as dic- Structuring and Stability of Solutions of the Static tated by Floquets theory. We also find evidence for greater Cahn-Hilliard Equation stability in a two-institution than a single institution set- ting. We relate these results to prior discussion of stability We use the variational form of the 2D Cahn-Hilliard equa- induced in bi-polar versus unipolar social systems. tion to obtain numerically the steady non-linear solutions of films of confined polymer blends with a free deformable Philip Poon surface. Varying the average composition and geometry Department of Mathematics of the films we find a rich morphology of solutions in the [email protected] form of laterally structured films, layered, droplets over the substrate and free surface, and checkerboard structures. David Krakauer, Jessica Flack We show that laterally structured films are energetically Center for Complexity & Collective Computation favorable and that most of the solutions appear through Wisconsin Institute for Discovery pitchfork bifurcations. [email protected], jcfl[email protected]

Santiago Madruga Aerospace Engineering School CP6 Universidad Polit´ecnica de Madrid Experimental Verification of Criteria for Escape [email protected] from a Potential Well in a Multi-degree of Free- DS15 Abstracts 95

dom System shells.

Criteria and routes of escape from a potential well have Timur Alexeev previously been determined for 1 degree of freedom (DOF) University of California, Davis mechanical systems with time-varying forcing, with rea- [email protected] sonable agreement with experiments. When there are 2 or more DOF, the situation becomes more complicated, but there is still a method, tube dynamics, for determining the CP7 phase space states which will escape. Here, we verify tube A New Mathematical Explanation of What Trig- dynamics for a 2 DOF experiment of a ball rolling on a gered the Catastrophic Torsional Mode of the surface. Tacoma Narrows Bridge

Shane D. Ross We suggest a mathematical model for the study of the dy- Virginia Tech namical behavior of suspension bridges which provides a Engineering Science and Mechanics new explanation for the appearance of torsional oscillations [email protected] during the Tacoma collapse.

Amir BozorgMagham Gianni Arioli University of Maryland, College Park Dipartimento di Matematica [email protected] Politecnico di Milano [email protected] Lawrence Virgin Cntr for Nonlinear and Complex Systems Duke University CP7 [email protected] Global Attractors for Quasilinear Parabolic- Hyperbolic Equations Governing Longitudinal Mo- tions of Nonlinearly Viscoelastic Rods CP6 Sensitivity of the Dynamics of the General We prove the existence of a global attractor and estimate Rosenzweig-MacArthur Model to the Mathemati- its dimension for a general family of third-order quasilinear cal Form of the Functional Response: a Bifurcation parabolic-hyperbolic equations governing the longitudinal Theory Approach motion of nonlinearly viscoelastic rods subject to interest- ing body forces and end conditions. The simplest version We revisit the Rosenzweig-MacArthur predator-prey model of the equations has the form wtt = n(wx,wxt)x where n to help explain sensitivity to the mathematical forms of is defined on (0, ∞) × R and is a strictly increasing func- three functional responses (Holling type II, Ivlev, and tion of each of its arguments, and with n →−∞as its Trigonometric). We consider both local and global dy- first argument goes to 0. This limit characterizes a total namics and determine possible bifurcations with respect compression, a source of technical difficulty, which delicate to variation of the carrying capacity of the prey. We pro- a priori estimates prevent. (These estimates simplify and vide an analytic expression that determines the criticality generalize earlier versions.) We determine how the dimen- of a Hopf bifurcation and revisit the ranking of the func- sion of the attractor varies with the several parameters of tional responses, according to their potential to destabilize the problem, giving conditions ensuring that it is small. the dynamics of the model. These estimates illuminate asymptotic analyses of the gov- erning equation as parameters approach limits. Gunog Seo Colgate University Suleyman Ulusoy [email protected] Zirve University [email protected] Gail Wolkowicz McMaster University Stuart S Antman [email protected] University of Maryland [email protected]

CP7 Numerical Simulations of Nonlinear Dynamics of CP7 Beams, Plates, and Shells Revision on the Equation of Nonlinear Vibration oftheCablewithLargeSag Solution of nonlinear structural dynamics poses a challeng- ing problem and often requires the use of computers in or- The problem in the conventional cable theory about the der to obtain a quantitative solution. Such simulations relation between the chord-line component of dynamical are usually computationally expensive and are typically cable tension and the deflection is discussed. The expres- performed only as academic research. The current study sion of the chord-line component of dynamical cable tension serves two purposes: i) it presents simple semi-implicit nu- is rationally revised based on the proposed compatibility merical formulations, which are computationally efficient, equation. The equation of motion of cable in time and simple to use, and can be used in nonlinear dynamics and space is then formulated with the corrected expression of chaos simulations ii) it serves as a good introduction to nu- chord-line component of cable internal force and reduced to merical studies of nonlinear structural dynamics for grad- nonlinear multi-degree-of-freedom system with Galerkin’s uate students and upper division undergraduate students. method. Some numerical results are presented and dis- Numerical formulations along with results are presented for cussed. The upper limit of the sag-span ratio for which the nonlinear oscillators, beams, von Karman plates, and thin conventional equation of cable motion can give acceptable 96 DS15 Abstracts

results is investigated. ics, and evaluated a range of questions involving spatial spread, alternative intervention strategies, and contribu- Kun Wang tions to transmission by different infectious stages (early- University of Macau stage, late-stage, and funeral transmission). [email protected] Marisa Eisenberg University of Michigan CP7 [email protected] Control Strategies for Electrically Driven Flapping of a Flexible Cantilever Perturbed by Low Speed Wind CP8 How Radiation-Induced Dedifferentation Influ- Control parameters for the effect of low speed wind per- ences Tumor Hierarchy turbations to the electrically driven flapping of a flexible cantilevered beam are studied both experimentally and nu- Evidence indicates solid tumors exhibit cellular hierarchy merically. The experiments consist of varying the applied where only a fraction of cells are able to maintain and re- potential (1kV-9kV) between the gap (15mm-35mm) sep- grow the tumor. Recent discoveries indicate that, besides arating a conducting plastic cantilever and a rigid ground these inherent cancer stem cells, other cells can dediffer- electrode. Other inputs are the frequency (1Hz-8Hz), the entiate to a stem-like state after radiation exposure. We input signal type (sine, square and triangle) and wind modify an ODE lineage model to include feedback, radia- speed (1mph-8mph). Numerical data is produced using tion, and dedifferentiation. Setting parameters with exper- the dynamic Euler-Bernoulli beam equation with viscous imental data, we observe an elevated dedifferentiation rate damping and gravitational effects. The electrical load ap- for irradiated cells that can profoundly impact long-term pears as a non-linear term in the otherwise linear equation. population size. The numerical and experimental data for the effects of elec- Kimberly Fessel trical load, frequency and wind speed on vibrational am- Mathematical Biosciences Institute plitude of the cantilever will be used to introduce control [email protected] strategies for these systems.

Thomas Ward John Lowengrub Department of Mechanical and Aerospace Engineering Department of Mathematics NC State University University of California at Irvine [email protected] [email protected]

CP8 CP8 Coexistence of Multiannual Attractors in a Disease Order Reduction and Efficient Implementation of Interaction Model: Whooping Cough Revisited Nonlinear Nonlocal Cochlear Response Models

Incidence of whooping cough (WC) exhibits variable dy- The cochlea is shown to exhibit active nonlinear spatiotem- namics with periodicity 2-5 years. We propose an alterna- poral response dynamics. To model such phenomena, it tive model of WC as interacting strains via age-dependent is often necessary to incorporate cochlear fluid-membrane convalescence. The model exhibits several stable multi- interactions. This results in both high-order model formu- annual coexisting attractors. Also, perturbation due to lations and computationally-intensive solutions that limit case-importation and noise in transmission switches the their practical use (for psychoacoustic audio signal pro- system from one dynamical regime to the other. This study cessing) even for simple single-tone brief inputs. In this suggests that variable dynamics of WC could be an emer- paper, we reformulate an existing nonlinear cochlear model gent property of the interacting system, which is not ob- into sparse state-space (SS) models that are of considerably served earlier. lower order (factor of 8) and are computationally simpler (factor of 25) with little reduction in accuracy. Samit Bhattacharyya NBHM, DAE, Research Fellow Maurice G. Filo Department of Pure Mathematics, University of Calcutta PhD Student at UC Santa Barbara [email protected] fi[email protected]

Matthew Ferrari, Ottar Bjornstad CP8 Penn State University Periodic Outbreaks in Models of Disease Transmis- [email protected], [email protected] sion with a Behavioral Response Recently there has been increasing interest in the effects CP8 of behavioral responses to information on outbreaks of in- Examining Ebola Transmission Dynamics and fectious diseases. Such a response can drive the infection Forecasting Using Identifiability and Parameter Es- to low endemic levels even if it wanes over time and the timation infection does not confer immunity upon recovery. This talk will report on recent results on the question whether The ongoing Ebola epidemic in West Africa is larger than a waning behavioral response provides sufficient protection all previous Ebola outbreaks combined. Here I will dis- against subsequent flare-ups of the infection. cuss our ongoing work developing mathematical models of the Ebola epidemic, using a range of identifiability and Winfried Just parameter estimation approaches. We used these mod- Department of Mathematics els to examine uncertainty in forecasting disease dynam- Ohio University DS15 Abstracts 97

[email protected] applications, will be given to illustrate the talk.

Joan Saldana John Hogan Departament d’Inform`atica, Matem`atica Aplicada i Bristol Centre for Applied Nonlinear Mathematics Estadstica Department of Engineering Mathematics, University of Universitat de Girona Bristol [email protected] [email protected]

Martin Homer CP8 University of Bristol Competition and Invasion of Dengue Viruses in Department of Engineering Mathematics Vaccinated Populations [email protected]

The complex competitive landscape that exists between the Mike R. Jeffrey, Robert Szalai four dengue serotypes will change in unforeseeable ways University of Bristol with the soon-to-be released commercial vaccines. Here, mike.jeff[email protected], [email protected] we use a compartmental dengue transmission model in- corporating mass vaccination to investigate the possibility of serotype reintroduction in locations where one or more CP9 serotypes are absent. We show that the widespread appli- Filippov Unplugged — Part 1 cation of fully sterilizing vaccines can have the unintended effect of facilitating the reintroduction of missing serotypes. Almost every paper on nonsmooth systems references the book by Filippov “Differential equations with discontinu- ous righthand sides’ (Kluwer, 1988). The aim of this talk is Luis Mier-y-Teran, Isabel Rodriguez-Barraquer to direct attention toward results therein that are relevant Johns Hopkins Bloomberg School of Public Health to the modern audience, yet do not appear to be widely [email protected], [email protected] known. In particular, we will focus on two-dimensional flows, and discuss how we must fundamentally revise our Ira B. Schwartz notions of singularities, codimension, separatrices, struc- Naval Research Laboratory tural stability, topological equivalence and bifurcations. Nonlinear Dynamical Systems Section [email protected] John Hogan Bristol Centre for Applied Nonlinear Mathematics Derek Cummings Department of Engineering Mathematics, University of Johns Hopkins Bloomberg School of Public Health Bristol [email protected] [email protected]

Martin Homer CP9 University of Bristol C∞ Regularisation of Local Singularities of Filippov Department of Engineering Mathematics Systems [email protected]

We study the Sotomayor-Teixeira regularization of a gen- Mike R. Jeffrey, Robert Szalai eral visible fold singularity of a Filippov system. In the case University of Bristol that the regularized system is Cp−1 the deviation from the p mike.jeff[email protected], [email protected] Fenichel manifold is O(ε 2p−1 ). We extend these results to the case where the regularized vector field is analytic. In this case the regularized vector field and the Filippov one CP9 are different in the whole phase space, but this is just a On the Use of Blow Up to Study Regularizations of technical problem that will not change the final result. Singularities of Piecewise Smooth Dynamical Sys- tems Carles Bonet Universitat Politecnica de catalunya This talk will demonstrate the use of the blow up method [email protected] of Krupa and Szmolyan to study the regularization of sin- gularities of piecewise smooth dynamical systems. We will Tere M. Seara-Alonso primarily focus on the regularization of the two-fold bi- Universitat Politecnica de Catalunya furcation and the perturbation of associated limit cycles, [email protected] pseudo-equilibria, and canard-like orbits connecting stable sliding with unstable sliding. We will also present results on how the regularization function can introduce additional CP9 bifurcation. Filippov Unplugged - Part 2 Kristian Uldall Kristiansen Following on from Filippov Unplugged part 1, we will Technical University of Denmark present results from ”Differential equations with discon- Department of Applied Mathematics and Computer tinuous righthand sides” that hold in n-dimensional nons- Science mooth systems. Focussing on issues of topological equiva- [email protected] lence and structural stability, we will identify basic topo- logical classes of singularities that can occur, as well as the John Hogan bifurcations that ensue. Practical examples, rooted in real Bristol Centre for Applied Nonlinear Mathematics 98 DS15 Abstracts

Department of Engineering Mathematics, University of School of Physics, Georgia Institute of Technology Bristol [email protected] [email protected] Predrag Cvitanovic Center for Nonlinear Science CP10 Georgia Institute of Technology Curve Evolution in Second-Order Lagrangian Sys- [email protected] tems

A second-order Lagrangian system is a generalization of a CP10 classical mechanical system for which the Lagrangian ac- tion depends on the second derivative of the state variable. Error Assessment of the Local Statistical Lineariza- Recent work has shown that the dynamics of such systems tion Method can be substantially richer than for classical Lagrangian systems. In particular, topological properties of the planar We determine probability density functions of multidimen- curves obtained by projection onto the lower-order deriva- sional stochastic differential equations by means of the tives play a key role in forcing certain types of dynamics. Local Statistical Linearization method. The core of this However, the application of these techniques requires an method is the approximation of a non-Gaussian probabil- analytic restriction on the Lagrangian that it satisfy a twist ity density by superposition of Gaussian densities. For this, property. Here we approach this problem from the point the evolutions of local Gaussian densities are calculated of view of curve shortening in an effort to remove the twist and used in a time stepping scheme. Moreover, we provide condition.We prove the existence of simple periodic solu- error evolutions using accurate Monte Carlo simulations, tions for a general class of systems without requiring the Stochastic Averaging and available analytical solutions. twist condition. Further, our results provide a framework in which to try to further extend the topological forcing Leo Dostal theorems to systems without the twist condition. Hamburg University of Technology Institute of Mechanics and Ocean Engineering Ronald Adams [email protected] Florida Atlantic University [email protected] Edwin Kreuzer Institute of Mechanics and Ocean Engineering William D. Kalies Hamburg University of Technology Florida Atlantic University [email protected] Department of Mathematical Sciences [email protected] CP10 R.C.A.M van Der Vorst Geometric Phase in the Hopf Bundle and the Sabil- Vrije Universiteit ity of Non-Linear Waves [email protected] Building on the Evans function, we have proven a related, alternative form of analysis that uses the Hopf bundle to CP10 determine the stability of traveling waves. The total space 2n−1 Tensor of Green of Coupled Thermoelastodynamics of the Hopf bundle is S and it is naturally embedded in Cn. The dynamical system associated with the linearized Some problems of coupled thermoelastodynamics are con- operator for a PDE induces a winding number through par- sidered. Method of boundary integral equations is used for allel transport in the fibre, S1. Our method uses parallel solution of system of integral equations, fundamental ten- transport to count the multiplicity of eigenvalues. sors of stresses received by using of apparate of generalized functions. Colin J. Grudzien University of North Carolina at Chapel Hill Bakhyt Alipova Mathematics Department University of Kentucky [email protected] [email protected] Christopher Krt Jones CP10 University of North Carolina at Chapel Hill [email protected] Periodic Eigendecomposition and Its Application in Nonlinear Dynamics CP10 As an extension of periodic Schur decomposition, periodic eigendecomposition is capable of calculating Floquet spec- Computation of Cauchy-Green Strain Tensor Using trum and Floquet vectors along periodic orbits in chaotic Local Regression systems accurately. Its effectiveness, and in particular its ability to resolve eigenvalues whose magnitude differs by The Cauchy-Green strain tensor provides an effective tool hundreds of orders, is demonstrated by applying the algo- for understanding unsteady flows. We propose a new rithm to computation of the full linear stability spectrum of method for computing the CG strain tensor using a local periodic solutions of Kuramoto-Sivashinsky system. Also, quadratic regression (LOESS) technique. We compare this its efficiency is compared with the existing covariant vec- LOESS method with several classical methods using closed tors algorithm. form flows, noisy flows, and simulated time series. In each case the CG strain tensor produced by the LOESS method Xiong Ding is remarkably accurate and robust compared to classical DS15 Abstracts 99

methods. being, a society .., are systems with memory (in many cases power-law). This implies a possibility of their description Shane D. Kepley by fractional differential equations or maps with power- Florida Atlantic University law memory. Nonlinear systems with power-law memory [email protected] demonstrate new features, including cascade of bifurca- tions type behavior (with fixed parameters). This behav- Bill Kalies ior could be related to the evolution of chronic diseases, Florida Atlantic University epileptic seizures, and evolution of the human society. In Department of Mathematical Sciences nonlinear systems with power-law memory chaos can be [email protected] controlled by changing nonlinearity parameter and also by changing a memory parameter of a system.

CP11 Mark Edelman Odd-Number Limitation for Extended Time- Stern College for Women and Courant Institute Delayed Feedback Control [email protected]

Time-delayed feedback control is a simple and estab- lished method to stabilize unstable periodic orbits within CP11 a chaotic attractor. Here we prove a generalization of the Discrete-Time Structure-Preserving Optimal Er- well-known odd-number limitation of this control method godic Control to the case of autonomous systems. This result is further generalized to the extended version of time-delayed feed- Trajectories are ergodic with respect to a measure when back control. We uncover the important role played by the amount of time spent in a neighborhood is propor- the period of the orbit that is induced by mismatching the tional to the measure evaluated over the neighborhood, delay time of the control scheme. making ergodicity an appropriate metric for searching a do- main. Ergodic control in higher dimensional configuration Andreas Amann,EdwardHooton spaces requires discretization of the optimal control formu- School of Mathematical Sciences lation. Recent works have shown advantages of structure- University College Cork preserving variational integrators in control and estimation [email protected], [email protected] of mechanical systems. Here we develop a discrete-time variational optimal ergodic control scheme. CP11 Kathrin Flakamp, Todd Murphey Approximate Controllability of An Impulsive Neu- Northwestern University tral Fractional Stochastic Differential Equation kathrin.fl[email protected], t- With Deviated Argument and Infinite Delay [email protected] We proved the approximate controllability of an impul- sive fractional stochastic neutral integro-differential equa- CP11 tion with deviated argument and infinite delay. We used Mathematical Study of the Effects of Travel Costs Schauder fixed point theorem and fundamental assump- on Optimal Dispersal in a Two-Patch Model tions on system operators. The inverse of controllability operator fails to exist in infinite dimensional space in case How might organisms constrained by perceptual limita- generated semigroup is compact. Therefore, the need to tions or imperfect information use resource information op- assume the invertibility of controllability operator is re- timally in habitat selection? We analyze a general ordinary moved. Lipschitz continuity is also not required. Specif- differential equation model of a single species in a two- ically we studied the following remote control dynamical patch heterogeneous environment. Global stability analy- system sis yields an evolutionarily stable information use strategy c q that depends on the magnitude of the constraints and the D [x(t)+g(t, xt)] = A[x(t)+g(t, xt)] + Bu(t)+f(t, x(a(x(t),t)),u(t)) t heterogeneity of the resources. Incorporating travel costs t into the model yields a different strategy that is locally + G(xs)dW (s),t∈ J =[0,T],t= convergenttk,k =1, ..., stable m −∞ x0(t)=φ(t),t∈ J1 =(−∞, 0] Theodore E. Galanthay + − University of Colorado x(t ) − x(t )=Ik(x(tk)),k=1, ..., m, k k [email protected]

Sanjukta Das CP11 Indian Institute of Technology, Roorkee, Computing Bisimulation Functions Using SoS Op- sanjukta [email protected] timization and δ-Decidability over the Reals

Dwijendra Pandey We present BFComp, an automated framework based Indian Institute of Technology, Roorkee on Sum-Of-Squares (SOS) optimization and δ-decidability [email protected] over the reals to compute Bisimulation Functions (BFs) that characterize input-to-output stability (IOS) of dynam- ical systems. BFs are Lyapunov-like functions that decay CP11 along the trajectories of a given pair of systems, and can Chaos in Biological Systems with Memory and Its be used to establish the stability of the outputs with re- Controllability spect to bounded input deviations. In addition to estab- lishing IOS, BFComp is designed to provide tight bounds Biological systems, a neuron, the brain, the heart, a human on the squared output errors between systems whenever 100 DS15 Abstracts

possible. For this purpose, two SOS optimization formu- Flows with Viscoelastic-Type Reynolds Stress lations and δ-decidability-based Satisfiability Modulo The- ory are employed. We illustrate the utility of BFComp on a Progress utilizing other closure protocols appear in this feedback-based canonical cardiac-cell model, showing that research and innovation. Although this article is moti- the four-variable Markovian model for the slow Potassium vated by challenges in partial differential equations, we current IKs can be safely replaced by an approximately consider a two-mode Faedo-Galerkin approximation(Ed one-variable Hodgkin-Huxley-type approximation. Lorenz ansatz sense) given by a system of singularly per- turbed ordinary differential equations in R4: Abhishek Murthy Philips Research North America dX [email protected] Ro = Y − EkX − λEkW, dt Md. Ariful Islam, Scott Smolka Computer Science dY = εX + X − Y − XZ, Stony Brook University dt [email protected], [email protected] dZ = −bZ + XY, Radu Grosu dt Vienna University of Technology [email protected] dW We = r(δλX − W ). dt

CP12 It is shown that the equilibrium point at the origin is asymptotically stable and attractive by the LaSalle in- Empirical Validation of Conceptual Climate Mod- variance principle. Utilizing center manifold calculations, els we show existence of supercritical pitchfork bifurcation and Poincare-Andronov-Hopf bifurcation. In order to uti- Conceptual climate models are useful for testing hypothe- lize geometric singular perturbation theory and Melnikov ses regarding the processes underlying observations; but techniques, we perturb the problem and carry the non- they generally can only qualitatively match the empirical linear analysis further to the question of the persistence records. Models based on substantially different underlying of inclination-flip homoclinic solutions. We present a geo- physics can have comparable correlations with any given metric approach to the problem which gives more refined a observation; more robust model validation procedures are priori energy type estimates on the position of the invari- needed. Using the Mid-Pleistocene Transition as a test ant manifold and its tangent planes as the manifold passes case, we will show how modern time-series-analysis tech- close to a normally hyperbolic piece of a slow manifold. niques can improve validation by extracting subtler fea- The main object of this result enables detection of chaotic tures of the observations and models. attractors in singularly perturbed dynamical systems as de- picted using the DsTool(Dynamical systems Tool) package Charles D. Camp,RyanSmith,AndrewGallatin program of Worfolk et al. California Polytechnic State University [email protected], [email protected], agal- Maleafisha Stephen Tladi [email protected] University of Limpopo, South Africa [email protected] CP12 Modified Lorenz Equations for Rotating Convec- CP12 tion Baroclinic Instability in An Initially Stratified Ro- tating Fluid We derive and examine systems of nonlinear differential equations similar to the Lorenz equations. In particu- Motivated by the large-scale atmospheric and oceanic cir- lar, starting from the partial differential equations describ- culation, we study the characteristics of density-driven con- ing two-dimensional Rayleigh-Benard convection we derive vective flow in an annular, tabletop-size rotating laboratory systems of ordinary differential equations that are slight tank, filled with water. Horizontal and vertical density gra- modifications of Lorenz’ original system. These new sys- dients are induced by differential heating at the sidewalls tems of equations incorporate the effects of rigid body ro- and salinity stratification, respectively. These boundary tation. We investigate the role that rotation has on the conditions, together with the rotation of the tank, yield dynamics of these reduced models. an interesting interplay between double-diffusive convec- tion and baroclinic instability. Jessica Layton BYU Miklos P. Vincze [email protected] HAS ELTE Theoretical Physics Research Group [email protected] Jared P. Whitehead, Shane McQuarrie Brigham Young University PatriceLeGal [email protected], IRPHE, CNRS-Aix Marseille [email protected] [email protected]

Uwe Harlander CP12 BTU Cottbus, Department of Aerodynamics and Fluid On the Geometry of Attractors in Ageostrophic Mechanics DS15 Abstracts 101

[email protected] linear stability analysis, numerical continuation, and di- rect numerical simulation. Heterogeneities in the natural frequency of the oscillators select the location of the co- CP12 herent clusters and may lead to their breakup. Pinning of Gradual and Abrupt Regime Shifts in Drylands traveling states by heterogeneities may occur, followed by depinning as the heterogeneity decreases. The response of ecosystems to climatic changes and an- thropogenic disturbances are crucial to our understanding Hsien-Ching Kao of these systems. Transitions in drylands due to these per- Wolfram Research Inc. turbations may take various forms, in particular due to the [email protected] patterned nature of patchy vegetation. I will discuss mul- tistability in these systems, owing to localized states and Jianbo Xie patterns with various wavelength, and possible transitions Department of Physics in them. A case study of fairy circles in Namibia will be University of California at Berkeley presented as a concrete example. [email protected] Yuval Zelnik Ben-Gurion University of the Negev Edgar Knobloch [email protected] University of California at Berkeley Dept of Physics [email protected] Ehud Meron Ben-Gurion University [email protected] CP13 Chimera States on the Route from Coherent State Golan Bel to a Rotating Wave Department of Solar Energy and Environmental Physics Ben-Gurion University We discuss the occurrence of chimera states on the route [email protected] from coherent via solitary states to the rotating wave in the networks of non-locally coupled pendulum-like nodes. We identify the wide region in parameter space, in which CP13 a new type chimera state, imperfect chimera state, which Localized States in Periodically Forced Systems is characterized by a certain number of oscillators escaped from synchronized chimeras cluster appears. We describe a The generalized Swift–Hohenberg equation with a novel mechanism for the creation of chimera states via the quadratic-cubic nonlinearity is used to study localized pat- appearance of the so-called solitary states. Our findings re- tern formation in the presence of time-periodic parametric veal that imperfect chimera states represent characteristic forcing. Regions of parameter space with distinct dynam- spatio-temporal patterns at the transition from coherence ics result from resonances between the period of the forcing to incoherence. and the time it takes the state to nucleate/annihilate wave- lengths of the pattern. The non-trivial structure of these Tomasz Kapitaniak regions can be understood qualitatively, and in some cases Technical University of Lodz quantitatively, by asymptotic arguments. Dept of Dynamic [email protected] Punit R. Gandhi Department of Physics University of California, Berkeley CP13 punit [email protected] Emergent Rhythmic Behavior of Mixed-Mode Os- cillations in Pulse-Coupled Neurons Cedric Beaume Imperial College London Our study is motivated by the experimental observation [email protected] of fast and slow rhythms in the mammalian olfactory sys- tem. We develop a minimal model in which the interac- Edgar Knobloch tion of three relevant populations of neurons is reduced to University of California at Berkeley an effective pulse-coupling within a single population of Dept of Physics mixed-mode oscillators. This pulse-coupling features mul- [email protected] tiple pulses with distinct propagation delays. We explore the dynamics of the system as a function of the shapes and delays of the pulses. CP13 Avinash J. Karamchandani Multicluster and Traveling Chimera States in Non- Department of Engineering Sciences and Applied local Phase-Coupled Oscillators Mathematics We study a nonlocal phase-coupled oscillator model in Northwestern University which chimera states develop from random initial condi- [email protected] tions. Several classes of chimera states have been found: (a) stationary multi-cluster states with evenly or unevenly James Graham distributed coherent clusters (b) a coherent state traveling Northwestern University with a constant speed or in a stick-slip fashion (c) chimera [email protected] states traveling with a constant speed. A self-consistent continuum description of these states is provided and their Hermann Riecke stability properties are analyzed through a combination of Applied Mathematics 102 DS15 Abstracts

Northwestern University Thorpe length. We discuss applications to ocean overflows. [email protected] Robert E. Ecke Center for Nonlinear Studies CP13 Los Alamos National Laboratory Onset and Characterization of Chimera States in [email protected] Coupled Nonlinear Oscillators Philippe Odier Role of symmetry breaking in nonlocal and global couplings ENS Lyon of networks of identical nonlinear oscillators for the occur- [email protected] rence of chimera mediated transitions between desynchro- nized and synchronized states will be discussed. We will also distinguish between amplitude chimera and frequency CP14 chimera states in this process and identify the conditions Effects of Fluid Dynamics on Experiments with under which chimera death states can arise. New rigorous Compressed/ Expanded Surfactant Monolayers quantitative measures to distinguish the above collective states in terms of strength of incoherence and discontinu- Monolayer experiments frequently measure surface rheo- ity measure will be presented. logical properties by periodically modulating surfactant concentration with two slightly immersed solid barriers Lakshmanan Muthusamy that control the free surface area of a shallow liquid layer. Centre for Nonlinear Dynamics, Department of Physics Because the modulation is slow, most theoretical studies Bharathidasan University, Tiruchirapalli 620024, India ignore fluid dynamics in the bulk. We present a long wave [email protected] theory that also takes fluid dynamics and symmetries into account. A nonlinear diffusion equation for surfactant con- centration that includes free surface deformation shows CP14 that fluid dynamics can be an important source of irre- Reduced Modeling of Exact Coherent States in versibility and help explain experimental observations. Shear Flow Maria Higuera In parallel shear flows, the lower branch solution follows E. T. S. I. Aeronauticos simple streamwise dynamics. A decomposition of this so- Univ. Politecnica de Madrid lution into Fourier modes in this direction yields modes [email protected] whose amplitudes scale with inverse powers of the Reynolds number. We use this scaling to derive a reduced model for Jose Perales exact coherent structures in general parallel shear flows. E. T. S. I. Aeronauticos The reduced model is regularized by retaining higher or- Universidad Politecnica de Madrid der viscous terms. Both lower branch and upper branch [email protected] solutions are captured and studied. Jose Vega Cedric Beaume E. T. S. I. Aeron´auticos Imperial College London Universidad Polit´ecnica de Madrid [email protected] [email protected]

Greg Chini Program in Integrated Applied Mathematics CP15 University of New Hampshire Noisy-Bar Problem [email protected] We have all experienced the inability to hear and under- Keith Julien stand our conversation partner in a crowded room. The Applied Mathematics difficulty tends to be most apparent in a crowded bar or a University of Colorado, Boulder club setting. Aside from presenting a social inconvenience, [email protected] this problem is also closely connected to the issue of signal to noise ratio in networked electronics. In this talk I will present a simple dynamical systems model that explains Edgar Knobloch the transition from a quiet to loud environment. University of California at Berkeley Dept of Physics Korana Burke [email protected] UC Davis [email protected] CP14 Stratified Shear Turbulence Experiments CP15 Embedology for Control and Random Dynamical We report experiments on stratified wall-bounded shear Systems flows in which we determine both the velocity and density fields. The flows undergo Kelvin-Helmholtz and Holmboe We introduce a data-based approach to estimating key instabilities depending on the strength of the stratification quantities which arise in the study of nonlinear control and shear. We characterize the instabilities by the Richard- systems and random nonlinear dynamical systems. Our son number dependence of a local Thorpe length that de- approach hinges on the observation that much of the ex- fines an intermittency fraction for the density interface and isting linear theory may be readily extended to nonlinear allows for an evaluation of the probability distribution of systems - with a reasonable expectation of success- once the DS15 Abstracts 103

nonlinear system has been mapped into a high or infinite [email protected] dimensional reproducing kernel Hilbert space. In particu- lar, we embed a nonlinear system in a reproducing kernel Hilbert space where linear theory can be used to develop CP15 computable, nonparametric estimators approximating con- Zero Density of Open Paths in the Lorentz Mirror trollability and observability energy functions for nonlinear Model for Arbitrary Mirror Probability systems, and study the ellipsoids they induce. It is then shown that the controllability energy estimator provides The Lorentz mirror model consists of a particle bounc- a key means for approximating the invariant measure of ing off randomly-oriented mirrors placed at integer lattice an ergodic, stochastically forced nonlinear system. In all points, and is thus a key model of deterministic dynamics cases the relevant quantities are estimated from simulated in a quenched random environment. We will present effi- or observed data. cient numerical simulations to count closed and open paths in the Lorentz mirror model, and arguments based on the Boumediene Hamzi results of those simulations [A.S. Kraemer & D.P. Sanders, Imperial College Journal of Statistical Physics 156, 908–916], to show that Department of Mathematics the density of open paths in a finite box tends to 0 as the [email protected] box size tends to infinity, for any probability p>0ofplac- ing a mirror at a point. Jake Bouvrie MIT David P. Sanders [email protected] Department of Physics, Faculty of Sciences National University of Mexico (UNAM) [email protected] CP15 Atahualpa Kraemer Faster Sensitivity Estimates for Stochastic Differ- Heinrich-Hein University of Dusseldorf ential Equations [email protected] Estimating the sensitivity of model predictions to param- eter variations is a common task in scientific computing. CP15 When the model in question takes the form of a stochastic Power System Stochastic Modeling differential equation, sensitivity estimates can be compu- tationally expensive, particularly if the system at hand is We develop and test recent methods in power systems sim- chaotic. In this talk, I will describe a class of algorithms ulation. A stochastic Runge-Kutta single-step solver is pro- for speeding up sensitivity estimates for models of noisy, posed; error coefficients and order conditions are derived. chaotic systems. A new method of retrieving the algebraic system variables after topological changes (i.e. line tripping) in the model Kevin K. Lin system is examined. The stability behavior of the system Department of Mathematics is studied under stochastic forcing and topological distur- University of Arizona bances. [email protected] Mathew Titus, Yue Zhang, Eduardo Cotilla-Sanchez Jonathan C. Mattingly Oregon State University Duke University [email protected], [email protected] [email protected], [email protected]

CP15 CP16 Noise Shaping and Pattern Discrimination in Re- Effects of Network Structure on the Synchroniza- current Spiking Neuronal Networks tion of Hamiltonian Systems

The enhancement of pattern discrimination is considered a Hamiltonian systems exhibiting long-range interactions are common step in early sensory processing by the brain, often frequently modeled using the Hamiltonian Mean Field attributed to a recurrent network. It has been suggested (HMF) model. Past research on the HMF has focused on that noise correlations arising from the common feedback the all-to-all case where each rotor is connected to every within recurrent spiking networks may interfere with the other rotor. We study the HMF on complex networks of intended pattern discrimination. We show that recurrent interactions amongst the rotors. We find that although excitatory-inhibitory networks with reciprocal connections, the network structure impacts the onset of rotor synchro- as they arise in the olfactory system, can reshape the noise nization and the path to synchrony, the maximum possible such that the network can enhance pattern discriminability synchrony is fairly independent of network structure. efficiently. Yogesh Virkar Hermann Riecke Department of Computer Science Applied Mathematics University of Colorado, Boulder Northwestern University [email protected] [email protected] Juan G. Restrepo Tom Zhao, Siu Fai Chow Department of Applied Mathematics Northwestern University University of Colorado at Boulder [email protected], siu- [email protected] 104 DS15 Abstracts

James D. Meiss the Friedlin-Wentzell action to predict and control noise- University of Colorado induced switching between different attracting states in ge- Dept of Applied Mathematics netic regulatory networks. We utilize this methodology to [email protected] identify new candidate strategies for cancer therapy in a coupled ODE model of the cell death pathway.

CP16 Daniel Wells Transient Spatiotemporal Chaos in a Network of Northwestern University Coupled Morris-Lecar Neurons Department of Engineering Sciences and Applied Mathematics Spatiotemporal chaos collapses to either a rest state or a [email protected] propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. The addition of William Kath weak excitatory synapses can increase the Lyapunov expo- Department of Applied Mathematics, Northwestern nent, expedite the collapse, and promote the collapse to University the rest state rather than the pulse state. A pulse solution Department of Neurobiology, Northwestern University may no longer be asymptotic for certain network topologies [email protected] and (weak) synapses. Renate A. Wackerbauer Adilson E. Motter University of Alaska Fairbanks Northwestern University Department of Physics [email protected] [email protected] CP16 Jacopo Lafranceschina Studies of Stable Manifolds of a Spatially Extended University of Alaska Fairbanks Lattice Kuramoto Model [email protected] We study the steady state solution of the 1D and 2D spatially extended Kuramoto model with nearest-neighbor CP16 coupling for a range of system sizes. Past the critical cou- Consequence of Symmetry Breaking in Two Cou- pling σc, different possible steady states can appear includ- pled Kuramoto Networks ing phase coherence (synchronization), and phase locking (traveling wave states). We characterize the terminal be- We explore symmetry breaking in a two-population Ku- havior of a space of initial conditions for a variety of bound- ramoto network, using the ansatz of Ott and Antonsen ary conditions: periodic, zero-flux and free. [Chaos 18, 037113 (2008)]. We find that the system is a generalized formulation for a single population of Andrea J. Welsh,FlavioFenton symmetrically-coupled, bimodally-distributed oscillators. Georgia Institute of Technology We explore this systems equilibria and invariant sets and [email protected], fl[email protected] characterize the bifurcations of both the incoherent and partially-coherent states. We then identify and break sev- eral symmetries present in this system, to see how the dy- CP17 namics change. Efficient Kernel Algorithm for the Dynamic Mode Scott T. Watson Decomposition of Observed Data George Mason University The dynamic mode decomposition (DMD) is a recently [email protected] proposed algorithm for decomposing time series data ob- served from nonlinear dynamical systems. We extend the Ernest Barreto DMD by using a statistical technique called the kernel George Mason University method. Our extended DMD can compute the mode de- Krasnow Institute composition significantly faster and more accurately than [email protected] other methods. In addition, we theoretically discuss the sufficient condition for the modes to be reconstructed from Bernard Cotton observed time series. We illustrate the validity and useful- George Mason University ness of our method by numerical examples. [email protected] Wataru Kurebayashi, Sho Shirasaka Paul So Tokyo Institute of Technology George Mason University [email protected], [email protected] The Krasnow Institute [email protected] Hiroya Nakao Graduate School of Information Science and Engineering, Tokyo Institute of Technology CP16 [email protected] Control of Stochastic and Induced Switching in Biophysical Complex Networks CP17 While the response of biological systems to noise has been Perturbing the Cat Map: Mixed Elliptic and Hy- studied extensively, there has been limited understand- perbolic Dynamics ing of how to exploit these fluctuations to induce a de- sired cell state. Here we present a method based on Arnolds cat map is a prototypical dynamical system with DS15 Abstracts 105

uniformly hyperbolic dynamics. We study a family of maps [email protected] homotopic to the cat map that has a saddle and a parabolic fixed point. Lerman conjectured that this map has a mixed phase space. We present some evidence in support. The CP17 elliptic orbits are confined to a channel bounded by mani- Classification of Critical Sets and Images for folds of the fixed points. The complement appears to have Quadratic Maps of the Plane positive measure with positive Lyapunov exponents. Real quadratic maps of the plane form a 12-parameter fam- James D. Meiss ily and exhibit a huge range of complicated dynamics. To University of Colorado consider the whole class of maps together, we consider only Dept of Applied Mathematics critical sets (J0) and their images (J1). J0 is a possibly de- [email protected] generate conic section. Possibilities for J1 are surprisingly restricted. We study this classification with a hierarchi- Lev Lerman cal structure - first via a normal form for homogeneous Lobachevsky State University of Nizhny Novgorod quadratic maps, and then for linear perturbations of these [email protected] homogeneous maps.

Bruce B. Peckham CP17 Dept. of Mathematics and Statistics University of Minnesota Duluth Invariant Manifolds and Space Mission Design in [email protected] the Restricted Four-Body Problem Chia-Hsing Nien Invariant manifolds play a crucial role in designing low- Department of Financial and Computational Mathematics energy trajectories of a spacecraft. We consider the four- Providence University Taichung City 43301 Taiwan body problem of Sun, Earth, Moon and a spacecraft by re- [email protected] garding the system as a coupled system of distinct RC3BPs with perturbations, namely, the systems of Sun-Earth- S/C+ (Moon perturb) and Earth-Moon-S/C+ (Sun per- Richard McGehee turb). We clarify tube-like invariant manifolds of each per- University of Minnesota turbed system and design a transfer trajectory from Earth [email protected] to Moon by patching trajectories associated with the in- variant manifolds. Bernd Krauskopf, Hinke M. Osinga University of Auckland Kaori Onozaki Department of Mathematics Waseda university [email protected], [email protected] [email protected] CP17 Hiroaki Yoshimura Waseday University The Existence of Horseshoe Dynamics in Three Di- [email protected] mensional Lotka-Volterra Systems

We prove the existence of horseshoe dynamics in three CP17 dimensional Lotka-Volterra systems. The proof uses a Shilnikov-type structure adapted to the geometry of the Mixing on a Hemisphere these systems.

Motivated by mixing in 3D rotated granular flows, we study Rizgar Salih, Colin Christopher the nonlinear dynamics of piecewise isometries (PWI) on a Plymouth University hemispherical shell for different rotation protocols. Map- [email protected], pings of singularities, termed the exceptional set, E,cover [email protected] the hemisphere’s surface in a variety of complex patterns and explain the ultimate degree of mixing but not the rate of mixing. To understand the mixing rate, we explore a CP18 Lyapunov exponent inspired method based on the parti- Inferring Causal Structures in Complex Systems tioning property of PWI. Via Causation Entropy

Paul Park Perhaps the most fundamental question in science in com- Northwestern University plex systems is to infer causes from influences between [email protected] many coupled elements. Empirically inferring causal struc- ture in complex systems by means of statistical and infor- Paul Umbanhowar, Julio Ottino mation theoretic techniques applied to time series data is a Northwestern University highly challenging and sensitive problem. We report here Evanston, IL 60208-3109 on our latest results of casual coupling inferences within [email protected], the framework of the Optimal Causation Entropy (oCSE) [email protected] approach, together with example applications.

Richard M. Lueptow Carlo Cafaro, Warren Lord, Jie Sun, Erik Bollt Northwestern University Clarkson University Department of Mechanical Engineering [email protected], [email protected], 106 DS15 Abstracts

[email protected], [email protected] tually interacting through ’social’ forces and forces from constraining walls and obstacles. In counterstreaming con- stricted flows, blocking evolves through a Hopf bifurcation CP18 into oscillatory flows. In flows around an obstacle, we find Robustness of Nonlinear Models that a simple local correlation term in the social force gives rise to hysteresis, with obstacle position as the parameter. We propose an algorithm to test the robustness to param- We have performed experiments to compare with the dy- eter variation of complex nonlinear models. In order to namical model. find the minimal parameter perturbation that can destroy a nominal solution, the algorithm uses numerical contin- Poul G. Hjorth uation techniques to move towards the closest bifurcation Technical Univ of Denmark point to the nominal parameter values, then solves a con- Department of Mathematics strained optimization problem to identify the closest point [email protected] of the bifurcation manifold to the nominal parameters. Jens Starke Fabio Della Rossa Technical University of Denmark Dipartimento di Elettronica, Informazione e Bioingegneria Department of Mathematics Politecnico di Milano [email protected] [email protected]

Alessandro Colombo CP18 Politecnico di Milano Dynamics of Correlated Novelties [email protected] One new thing often leads to another. Kauffman and oth- Fabio Dercole, Carlo Piccardi ers have hypothesized that this correlation between novel- Dipartimento di Elettronica, Informazione e Bioingegneria ties is important for understanding anything that evolves: Politecnico di Milano life, technology, language, etc. Ill discuss a simple model [email protected], [email protected] that predicts the dynamical fingerprints of correlated nov- elties (they take the form of certain statistical signatures) and then test the predictions against enormous data sets of CP18 human activity (listening to songs, writing words in books, A New Filter for State Estimation in Neural Mass making up tags, and editing Wikipedia pages). Models Steven H. Strogatz The presentation will introduce a new filter for state es- Cornell timation of neural mass models. The ability to estimate [email protected] and track states in large-scale neural models is critical for developing robust therapies via model-based feedback con- trol using electrical stimulation. Model-based control is CP18 particularly important for diseases such as epilepsy, where Systems with Hidden Slow Fast Dynamics pathologies are highly patient-specific. The new filter is similar to the unscented Kalman filter, where a Gaussian Examples of biochemical systems with complicated non- approximation is used. However, the mean and covariance obvious slow fast structures will be presented. In suitable of the state estimates are propagated analytically. The an- scalings or blow-ups hidden slow manifolds organizing the alytic results lead to an increase in estimation accuracy and dynamics can be found and utilized in the analysis of the a decrease in computational demands. The development of dynamics. the new methods presented in this presentation will facili- Peter Szmolyan tate the development of large-scale patient-specific compu- Institute for Analysis and Scientific Computing tational model of neurological diseases and open the door Vienna University of Technology to the possibility of novel therapies. [email protected] Dean R. Freestone University of Melbourne, Australia CP19 & The Bionics Institute, Melbourne, Australia [email protected] A Dynamical and Algebraic Study of a Family of Lienard Equations Transformable to Riccati Equa- tions Philippa Karoly, Dragan Nesic, Mark Cook The University of Melbourne In this talk we present some algebraic and dynamical re- [email protected], sults corresponding to the five parameter differential equa- [email protected], [email protected] tion

 2k m−k−1 2m−2k−1  dy David Grayden yy =(αx + βx )y + γx y = , University of Melbourne, Australia dx & The Bionics Institute, Melbourne, Australia being a, b, c ∈ C, m, k ∈ Z and [email protected] m+k−1 m−k−1 4k 2k α = a(2m+k)x β = b(2m−k)x ,γ= −(amx +cx +bm). CP18 This equation is a foliation of a five parameter Lienard Hysteresis Effects in Pedestrian Flows equation, which is transformed into a Riccati equation. These transformations are used to do an algebraic analy- We model a crowd of pedestrians as point particles mu- sis about the obtaining of explicit solutions (in differential DS15 Abstracts 107

Galois sense) of the Lienard equation, as well the obtain- School of Physics and Center for Nonlinear Science ing of some elements from Darboux theory of integrability: [email protected] invariant algebraic curves, first integrals, cofactors, etc.. of the Lienard vector field. Finally, a qualitative analysis Predrag Cvitanovic is presented (type of critical points, Lyapunov functions, Center for Nonlinear Science etc..) Georgia Institute of Technology [email protected] Primitivo B. Acosta-Humanez, Jorge Rodriguez-Contreras, Alberto Reyes-Linero Universidad del Atlantico CP19 [email protected], [email protected], Metric Invariance Entropy and Conditionally In- [email protected] variant Measures

Invariance entropy is a measure for the data rate needed CP19 to make a subset of the state space of a control systems New Asymptotics of Homoclinic Orbits Near invariant. Here a notion of metric invariance entropy is Bogdanov-Takens Bifurcation Point constructed with respect to a conditionally invariant mea- sure for control systems in discrete time. It is shown that We derive explicit asymptotics for the homoclinic orbits the metric invariance entropy is an invariant under conju- near a generic Bogdanov-Takens (BT) point, with the aim gations and that the topological invariance entropy (also to continue the branch of homoclinic solutions that is called feedback entropy) provides an upper bound. rooted in the BT point in parameter and state space. We present accurate second-order homoclinic predictor of the Fritz Colonius homoclinic bifurcation curve using a generalization of the University of Augsburg Poincar´e-Lindstedt (P-L) method. We show that the P-L [email protected] method leads to the same homoclinicity conditions as the classical Melnikov technique, the branching method and the regular perturbation method (R-P). The R-P method CP19 shows a “parasitic turn” near the saddle point. The new A Fast Explicit Method for Computing Invariant asymptotics based on P-L do not have this turn, making it Solutions of High-Dimensional Dynamical Systems more suitable for numerical implementation. We show how with Continuous Symmetries to use these asymptotics to calculate the initial homoclinic cycle to continue homoclinic orbits in two free parame- Given a dynamical system with a continuous symmetry, we ters. The new homoclinic predictors are implemented in construct a perturbed system whose trajectories converge the Matlab continuation package MatCont to initialize the to the invariant solutions of the original dynamical system. continuation of homoclinic orbits from a BT point. Several The perturbation term is a measure of the curvature of the examples in the case of multidimensional state spaces are trajectories and is readily computable from the equations included. of motion. The computational cost is therefore reduced considerably compared to algorithms based on Newton’s Bashir M. Al-Hdaibat iterations or variational methods. Dept. of Applied Math., Computer Science and Statistics Gent University, Belgium Mohammad Farazmand [email protected] Mathematics, ETH Zurich [email protected] Willy Govaerts Ghent University Predrag Cvitanovic [email protected] Center for Nonlinear Science Georgia Institute of Technology Yuri Kuznetsov [email protected] Department of Applied Mathematics, University of Twente, The Netherlands [email protected] CP19 Dimensionality Reduction of Collective Motion by Hil Meijer Principal Manifolds Twente University, NL [email protected] Current nonlinear dimensionality reduction methods as ap- plied to collective motion of agents may exhibit unfaithful embedding, due to limitations of control over the map- CP19 ping between original and embedding spaces. We propose Periodic Orbit Theory of Continuous Media an alternative approach by minimizing the orthogonal er- ror while topologically summarizing the high-dimensional Nonlinear PDEs of a wide range, from Navier-Stokes equa- data. We construct embedding coordinates in terms of tions for viscous fluids to the Yang-Mills equations for geodesic distances along smoothed principal curves, such gauge fields, can exhibit chaos. One can use high dimen- that, the mapping between original and embedding spaces sional exact coherent solutions of these systems to predict is defined in terms of local coordinates. physical observables by utilizing trace sums over relative periodic orbits. These trace formulas are exact for classical Kelum D. Gajamannage systems, but, as we shall demonstrate on several applica- Clarkson University tions, their convergence can be highly nontrivial. [email protected]

Nazmi Burak Budanur Sachit Butail 108 DS15 Abstracts

Indraprastha Institute of Information Technology Delhi it is clear that surface curvature can have nontrival and [email protected] surprising effects.

Maurizio Porfiri Frits Veerman Dept. of Mechanical, Aerospace and Manufacturing Mathematical Institute Engineering University of Oxford Polytechnic University [email protected] mporfi[email protected] Philip K. Maini Erik Bollt Centre for Mathematical Biology Clarkson University University of Oxford [email protected] [email protected]

CP20 CP20 On the Numerical Integration of One Nonlinear Nonlinear Behaviors As Well As Bifurcation Mech- Parabolic Equation anism in Switched Dynamical Systems

In the present paper author considers initial-boundary Dynamical model of a typical centrifugal flywheel governor problem to following nonlinear parabolic equation: system with periodic switches between two forms of exter- nal torque has been established. Two types of bifurcation ∂U ∂ ∂U ∂U can be observed in the autonomous subsystem, where the = k +f (x, t, U) , (x, t) ∈ (0, 1)×(0,T] ,T>0. ∂t ∂x ∂x ∂x Hopf bifurcation may lead to the occurrence of periodic oscillation, while the fold bifurcation may result in the dis- For the mentioned problem author constructs the corre- appearance of the equilibrium points. The dynamics often sponding difference scheme and in certain conditions proves behaves in periodic oscillations with the same frequency the convergence of its solution to the solution of the source as the periodic switch. Generalized Hopf bifurcation may problem with the convergence rate O τ + h2 .Forthe lead to the alternation of the behaviors between periodic same difference scheme in the same conditions the exis- movements and quasi-periodic oscillations. tence and uniqueness of its solution is proved. Yu V. Wang Mikheil Tutberidze York College, The City University of New York Ilia State University [email protected] Associated Professor [email protected] CP20 Gpu-Based Computational Studies of the Interac- CP20 tion Between Reentry Waves and Gap Junctional A Continuous Model for the Pathfinding Problem Uncoupling in Cardiac Tissues with Self-Recovery Property The obstruction of coronary flow can cause cardiac arrhyth- We propose a model which is capable of finding a path con- mias including ventricular tachycardia and ventricular fib- necting two specified vertices which are connected by uni- rillation. Gap junctional uncoupling associates with this directional edges. The system has a self-recovery property, process but to date the detailed underlying mechanism re- i.e., the system can find a path when one of the connections mains unclear. Our project investigates the dynamic re- in the existing path is suddenly terminated. lationship between gap junctional uncoupling and cardiac arrhythmia using GPU computing. This study promises to Kei-Ichi Ueda deepen our understanding of this phenomenon and could Faculty of Science, University of Toyama enable us to control cardiac arrhythmia by manipulating [email protected] the gap junctional coupling.

Masaaki Yadome Zhihui Zhang WPI-AIMR, Tohoku University Florida State University [email protected] [email protected]

Yasumasa Nishiura RIES, Hokkaido University CP21 Japan β1-Adrenergic Regulation of Action Potential and [email protected] Calcium Dynamics in a Model of Mouse Ventricu- lar Myocytes

CP20 A detailed experimentally-based compartmentalized model Patterns on Curved Backgrounds: the Influence of of the β1-adrenergic signaling system in mouse ventricu- Local Curvature on Pattern Formation lar myocytes is developed. Model simulations reproduced experimental data on phosphorylation dynamics of major We indicate how the concepts and approaches developed ionic currents and calcium binding proteins, voltage-clamp in the context of the (linear) theory of patterns on flat data on ionic currents, modulation of the cardiac mouse ac- 2 backgrounds (such as R ) can be extended to more general tion potential and calcium transients by the β1-adrenergic surfaces with nonvanishing curvature. The influence of lo- signaling system. Action mechanisms of phosphodiesterase cal curvature on the appearance and dynamics of patterns and protein kinase A inhibitors on the mouse action po- is demonstrated by a number of example surfaces, where tential and calcium dynamics at the cellular level are dis- DS15 Abstracts 109

cussed. [email protected], [email protected]

Vladimir E. Bondarenko Department of Mathematics and Statistics CP21 Georgia State University Spike Time Dependent Plasticity in a Spiking Neu- [email protected] ral Network

To determine which inputs for a neuron are important and CP21 whichinformationaneuronshouldlistentoisanimportant A Mathematical Model for Frog Population problem during brain development and during learning. Dynamics with Batrachochydrium Dendrobatidis Spike-Timing Dependent Plasticity (STDP) is a physio- (Bd) Infection logical adaptation mechanism of synaptic regulation which make a neuron to determine which neighboring neurons Chytridiomycosis is a disease that poses a serious threat to are worth by potentiating those inputs and depressing the frog populations worldwide. Several studies confirmed that other. We work on obtaining a good mathematical under- inoculation of Janthinobacterium lividum (Jl) can inhibit standing of Spike-Timing Dependent Plasticity (STDP). the disease. In this talk, I present a mathematical model This involves understanding why STDP works so well and of a frog juvenile-adult population infected with chytrid- the significance of factors like STDP type, learning window iomycosis caused by the fungal pathogen Batrachochydrium and scaling under increasing network size. The mathemati- dendrobatidis (Bd) to investigate on how the inoculation of cal model we construct, by using phase oscillators is a good anti-Bd bacterial species Jl could reduce Bd infection on example of discrete adaptive asynchronous network. This frogs. is a joint work with Mike Field from Rice University.

Baoling Ma Anushaya Mohapatra University of Louisiana - Lafayette Oregon State University [email protected] [email protected]

CP21 Mike Field Rice University Houston A Model of Heart Rate Dynamics for Changes in mikefi[email protected] Exercise Intensity Chris Bick A nonlinear dynamical systems model for heart rate is in- Rice University vestigated for changes in exercise intensity. The model [email protected] equilibria are used to determine the instantaneous heart rate of an individual during acute bouts of exercise that vary in intensity (power output) and cadence. Theoretical CP22 predictions show good agreement with laboratory cycling tests that were performed on several healthy adults. Computational Topology Techniques for Charac- terizing Time Series Data MichaelJ.Mazzoleni Duke University Full and accurate reconstruction of dynamics from time- [email protected] series data—e.g., via delay-coordinate embedding—is a real challenge, but useful information can be gleaned from Claudio Battaglini incomplete embeddings. We apply computational topol- University of North Carolina at Chapel Hill ogy to a sequence of lower-dimensional embeddings of the [email protected] data. Even though the full topology cannot be computed from these incomplete reconstructions, we conjecture that there are some results that can be computed from a se- Brian Mann quence Duke University of such reconstructions, and that these are useful [email protected] in time-series analysis. Elizabeth Bradley CP21 University of Colorado Department of Computer Science The Evolutionary Dynamics of Gamete Recogni- [email protected] tion Genes James D. Meiss Fertilization of gametes in broadcast spawners such as sea University of Colorado urchins and abalone is modeled as a random walk process Dept of Applied Mathematics with successful fertilization depending on variables such as [email protected] binding efficiency, sperm and egg concentration, and phys- ical characteristics of gametes. We develop a dynamical system modeling the evolution of binding genes and illus- Joshua T. Garland trate the conditions under which less efficient binding is fa- University of Colorado at Boulder vored. The stability of different binding strategies exhibits Department of Applied Mathematics a complex series of bifurcations with increasing sperm con- [email protected] centration. Nicole Sanderson David Mcavity, Mottet Geneva University of Colorado The Evergreen State College Department of Mathematics 110 DS15 Abstracts

[email protected] Department of Mechanical Engineering [email protected], [email protected]

CP22 Plankton Models with Time Delay CP23 Noise and Determinism of Stimulated Brillouin We consider a three compartment (nutrient- Scattering Dynamics in Optical Fiber phytoplankton-zooplankton) model with nutrient re- cycling. When there is no time delay the model has a Stimulated Brillouin scattering (SBS) is a noise-initiated conservation law and may be reduced to an equivalent two nonlinear optical phenomenon that occurs in optical fiber. dimensional model. We consider how the conservation law We present numerical modeling and experimental observa- is affected by the presence of a state dependent time delay tions of SBS in single-mode optical fiber. We employ sev- in the model. We study the stability and bifurcations of eral statistical methods to quantify and examine the roles equilibria when the total nutrient in the system is used as of determinism and stochasticity of SBS using time-delay the bifurcation parameter. embedding, false near neighbors and Hurst exponents. Ex- perimental and theoretical results display a transition in Sue Ann Campbell the nature of statistical fluctuation properties from lower University of Waterloo to higher input powers. Dept of Applied Mathematics [email protected] Diana A. Arroyo-Almanza Institute of Physical Science and Technology, Matt Kloosterman University of Maryland Dept of Applied Mathematics [email protected] University of Waterloo [email protected] Rafael Setra, Zetian Ni University of Maryland Francis Poulin rafawaffl[email protected], [email protected] Department of Applied Mathematics University of Waterloo Thomas E. Murphy [email protected] University of Maryland, College Park Dept. of Electrical and Computer Engineering [email protected] CP22 Noise, Chaos and Entropy Generation in a Time- Rajarshi Roy Delayed Dynamical System University of Maryland [email protected] Dynamical chaos and single photon detection are two phys- ical sources of randomness employed to generate fast, cryp- tographically secure random numbers. We present an ex- CP23 perimental system with both types of randomness: an Vector Rogue Waves and Dark-Bright Boomeronic electro-optic feedback loop incorporating a single-photon Solitons in Autonomous and Non-Autonomous Set- detector. We describe how the dynamics change from shot tings noise to deterministic chaos as the photon rate increases, and how the entropy rate can reflect either chaos or shot In this talk, I will discuss the dynamics of vector rogue noise depending on sampling rate and resolution. waves and dark-bright solitons in two-component non- linear Schr¨odinger (NLS) equations with variable coeffi- Aaron M. Hagerstrom,RajarshiRoy cients. Using a suitable transformation for the wave func- University of Maryland tions, the two-component NLS system is converted into the [email protected], [email protected] well-known integrable Manakov system. Then, the vector rogue and dark-bright boomeron-like soliton solutions of Thomas E. Murphy the latter are converted back into ones of the original non- University of Maryland, College Park autonomous model. Using direct numerical simulations, Dept. of Electrical and Computer Engineering I will present the formation and existence of such soliton [email protected] solutions in the non-autonomous case.

Efstathios Charalampidis CP22 Department of Mathematics and Statistics Stochastic Delay in Gene Regulation: Exact Sta- University of Massachusetts, Amherst bility Analysis [email protected]

Gene regulatory networks consist of interacting genes and R. BABU Mareeswaran, T. Kanna proteins and they control the response of cells to envi- Post Graduate and Research Department of Physics ronmental stimuli. The biochemical reactions involved in Bishop Heber College, India gene expression take finite time which lead to time delays babu nld@rediffmail.com, kanna [email protected] that vary stochastically due to the inherent intracellular noise. In this talk we analyze the dynamics of systems with stochastic delays and derive exact stability conditions Panayotis Kevrekidis of equilibria based on the second moment dynamics. University of Massachusetts [email protected] Mehdi Sadeghpour, Gabor Orosz University of Michigan, Ann Arbor Dimitri Frantzeskakis DS15 Abstracts 111

University of Athens σ, t+τ). From an initial set of such solutions we obtain a se- [email protected] quence of new sets of invariant solutions via numerical con- tinuation along paths in the parameter space of the CGLE. Solutions are obtained by solving an underdetermined sys- CP23 tem of nonlinear algebraic equations resulting from use of Control of Extreme Events in the Bubbling On- a spectral-Galerkin discretization in both space and time set of Wave Turbulence in the Forced and Damped of the CGLE and the use of a path following method. The Non-Linear Schr¨odinger Equation set of initial solutions led to distinct, new invariant solu- tions of the CGLE in the final parameter region. All the The existence of high amplitude intermittent fluctuation solutions are unstable, and have multiple modes and fre- in many non-linear dynamical systems constitutes a prob- quencies active, respectively, in their spatial and temporal lem of great relevance in different fields of science. In this spectra. Symmetry gaining/breaking behavior associated work we show the existence of an intermittent transition with the spatial reflection symmetry A(x, t) → A(−x, t) from temporal chaos to turbulence in a spatially extended was common in the parameter regions traversed. dynamical system, namely the forced and damped one- dimensional non-linear Schr¨odinger equation. For some Vanessa Lopez values of the forcing parameter the system dynamics in- IBM Watson Research Center termittently switches between ordered states and turbu- [email protected] lent states, which may be seen as extreme events in some contexts. In a Fourier phase-space the intermittency takes place due to the loss of transversal stability of unstable CP23 periodic orbits embedded in a low-dimensional chaotic at- Nonlinear Oscillations and Bifurcations in Silicon tractor. We mapped these transversely unstable regions Photonic Resonators and locally perturbed the system in order to significantly reduce the occurrence of extreme events of turbulence. Silicon microdisk resonators are micron-scale optical de- vices in which optical, thermal, electron/hole, and mechan- Paulo Galuzio ical effects interact to produce a wide range of dynamical Department of Physics phenomena. In the strongly nonlinear regime, we demon- Federal University of Parana strate the presence of Hopf and homoclinic bifurcations ppg06@fisica.ufpr.br leading to the onset and destruction of self-sustained os- cillations. We further show that the six-dimensional sys- Ricardo L. Viana tem of equations governing microdisk behavior can be re- Departmento de Fisica duced to a nearly-one-dimensional relaxation-oscillator sys- Federal University of Parana tem, and qualitative dynamics are well represented by a toy viana@fisica.ufpr.br model. Alexander Slawik,DanielAbrams Sergio R. Lopes Northwestern University Department of Physics [email protected], Federal University of Parana [email protected] lopes@fisica.ufpr.br

CP24 CP23 Finding the Stokes Wave: From Low Steepness to Reducibility of One-dimensional Quasi-periodic Almost Limiting Wave Schr¨odinger Equations A Stokes wave is a fully nonlinear wave that travels over Consider the time-dependent linear Schr¨odinger equation the surface of deep water. We solve Euler equations with i˙qn = (qn+1+qn−1)+V (x+nω)qn+δ amn(θ+ξt)qm,n∈freeZ, surface in the framework of conformal variables via m∈Z Newton Conjugate Gradient method and find Stokes waves in regimes dominated by nonlinearity. By investigating where V is a nonconstant real-analytic function on T , ω Stokes waves with increasing steepness we observe peculiar satisfies a certain Diophantine condition and amn(θ)is oscillations occur as we approach Stokes limiting wave. Fi- b real-analytic on T , b ∈ Z+, decaying with |m| and |n|. nally by analysing Pade approximation of Stokes waves we We prove that, if  and δ are sufficiently small, then for infer that analytic structure associated with those waves b a.e. x ∈ T and “most” frequency vectors ξ ∈ T ,itcan has branch cut nature. be reduced to an autonomous equation. Moreover, for this non-autonomous system, “dynamical localization” is main- Sergey Dyachenko tained in a quasi-periodic time-dependent way. University of Arizona [email protected] Jiansheng Geng Nanjing University [email protected] CP24 Blow-Ups in Nonlinear Pdes, Composite Grid- Particle Methods, and Stochastic Particle Systems CP23 Numerical Continuation of Invariant Solutions of I will discuss a numerical method best suited for solving the Complex Ginzburg-Landau Equation evolution PDEs exhibiting singular and multiscale behavior (shocks or blow-ups). This method employs representation We compute solutions of the complex Ginzburg-Landau of solution simultaneously as a field (discretized on a grid equation (CGLE) invariant under the action of the 3- or via finite elements) and a particle system. The field dimensional Lie group of symmetries A(x, t) → eiθA(x + and the particles exchange mass according to criteria based 112 DS15 Abstracts

on the types of singularities that are formed in a given liquid micro flows is captured using viscous potential flow system. Examples with Keller-Segel equations of bacterial (VPF) theory. A linear stability analysis is carried out chemotaxis, Fisher-Kolmogorov, Burgers, and a few other and the jetting to bubbling transition is predicted using equations will be presented. the Briggs criterion of absolute-convective instability tran- sition. We study the effect of the wide parameter space Ibrahim Fatkullin (Reynolds number, Weber number, density ratio, viscosity University of Arizona ratio and confinement) on this transition. Department of Mathematics [email protected] Dipin S. Pillai Ph.D. Scholar Indian Institute of Technology Madras, India CP24 [email protected] Singularities of the Stokes’ Wave: Numerical Sim- ulation S. Pushpavanam Professor Two-dimensional potential flow of the ideal incompressible Indian Institute of Technology Madras, India fluid with free surface and infinite depth can be described [email protected] by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with constant velocity. CP25 Alexander O. Korotkevich Finding Model Parameters Without Prior Knowl- Dept. of Mathematics & Statistics, University of New edge of Solve-Able Regions: A Solar Thermochem- Mexico istry Case-Study L.D. Landau Institute for Theoretical Physics RAS [email protected] Reduction of cobalt oxide nanoparticles is the first step in a solar thermochemical process to sustainably produce hy- drogen from water with concentrated sunlight. Using non- CP24 isothermal reaction data from the process as a case-study, Branch Cut Singularity of Stokes Wave we demonstrate a two-stage particle-swarm optimization method to find kinetic parameters in the shrinking core Stokes wave is the fully nonlinear gravity wave propagating model without a valid initial guess or bounding under mul- with the constant velocity. We consider Stokes wave in tiple, simultaneous rate-limiting conditions. The technique the conformal variables which maps the domain occupied developed is broadly applicable to identifying parameters by fluid into the lower complex half-plane. Then Stokes in data-fitting numerically intractable models. wave can be described through the position and the type of complex singularities in the upper complex half-plane. Karl Schmitt University of Maryland, College Park Pavel M. Lushnikov Dept. of Mathematics, AMSC Department of Mathematics and Statistics [email protected] University of New Mexico [email protected] Luke Venstrom Valparaiso University Dept. of Mechanical Engineering CP24 [email protected] Coupled Parametrically Forced Oscillators and Modulated Cross-Waves William D. Arloff Valparaiso University Recent experiments and theory for subharmonic cross- william.arloff@valpo.edu waves in horizontally vibrated containers found slowly modulated (quasiperiodic) solutions that cycle between balanced and one-sided excitation. We analyze a gener- Leandro Jaime alized model of coupled parametrically forced oscillators Valparaiso University with arbitrary relative phase to understand how these so- Dept. of Mechanical Engineering lutions arise, depending on coupling and forcing, and re- [email protected] late this to an exchange symmetry permitted by specific forcing phases. A complex bifurcation scenario involving secondary modes and homoclinic bifurcations emerges in CP25 many cases. Experiments on a Pinball-Like Oscillator

Jeff Porter, Pablo Salgado Sanchez, Ignacio Tinao, Ana The response of a harmonically-excited mechanical system Laveron-Simavilla in which a severe nonlinearity occurs due to an impact is Universidad Politecnica de Madrid presented. The system receives a discrete input of energy jeff[email protected], [email protected], at the impact condition: it is kicked. This is reminiscent of [email protected], [email protected] the unpredictability of the classic pinball machine. Close correlation is obtained between a mechanical experiment and numerical simulation, including unusual bifurcation se- CP25 quences and co-existing responses. Jetting-BubblingTransition in Microflows Lawrie N. Virgin Gas-liquid flows in microchannels are found to be primarily Department of Civil and Environmental Engineering of two types - jetting and bubbling. The dynamics of gas- Duke University DS15 Abstracts 113

[email protected] [email protected]

CP25 CP26 Exploring the Hyperbolicity of Chaotic Rayleigh- How Monetary Policy Can Cause Forecasting Un- B´enard Convection certainty

Covariant Lyapunov vectors allows us to quantify the di- Federal Reserve Chairwoman Yellen seems to be guided rection of the stable and unstable manifolds of the tan- by a rule that keeps interest rates low (high), when the gent space for the high-dimensional chaotic dynamics of economy is operating below (above) its trend. Instead of Rayleigh-B´enard convection. The principal angle between stabilizing the economy, the unintended consequence of the these manifolds can be used to determine the hyperbolicity Yellen Rule is greater uncertainty, due to nonlinear feed- of the dynamics. We use numerical simulations to compute back. The resulting forecast errors can be modeled by the covariant Lyapunov vectors of Rayleigh-B´enard convec- applying a Sprott nonlinear dynamical system of simple tion to probe fundamental features of the dynamics of an chaos, perturbed by random noise and shocked by excess experimentally accessible and high-dimensional system. demand for real money.

Mu Xu, Mark Paul James M. Haley Department of Mechanical Engineering Point Park Universtiy Virginia Tech [email protected] [email protected], [email protected]

CP26 CP25 Non-Smooth Dynamics and Bifurcations in a Snakes on An Invariant Plane: Coupled Model of Electricity Market Translational-Rotational Dynamics of Flying Snakes This paper proposes a model for the supply and demand of electricity in a domestic market based on system dynam- Flying snakes of the genus Chrysopelea use body flattening ics. Additionally, the model shows piecewise-smooth dif- and three-dimensional body undulations in a dynamic yet ferential equations. Mathematical analysis and simulation controlled glide through air. Given this complexity, salient explain some counter-intuitive dynamics which also were body dynamics relevant to glide stability are unknown. detected in practice. Then, a general model is proposed, We investigate a tandem airfoil model with snake-like fea- which is closer to real electricity markets. Discontinuities tures to better understand aerodynamic effects of undu- have a large effect on the qualitative analysis. A first result lation and translational-rotational mechanical coupling on to be noted is the use of asynchronous maps for understand- motion and stability during a glide. We elucidate some ing what happens when parameters are varied, leading to dynamical phenomena that occur including bifurcations, non-smooth bifurcations. To our knowledge. there are still limit cycles, and a gliding manifold. no reports in the literature about its use in socio-economic market systems. The other noteworthy result in this re- Isaac Yeaton, Hodjat Pendar, Jake Socha search is the effect that the ROI (Investment returns) has Virginia Tech on the system dynamics since it leads to different surfaces [email protected], [email protected], [email protected] whose slope change according to the parameters.

Shane D. Ross Gerard Olivar Tost Virginia Tech Department of Mathematics and Statistics Engineering Science and Mechanics Universidad Nacional de Colombia - Manizales [email protected] [email protected]

Johnny Valencia Calvo CP26 Ph.D Candidate in Systems Engineering and Computer Constant Rebalanced Portfolio Strategy Is Ratio- Sciences nal in a Multi-Group Asset Trading Model School of Mines - Universidad Nacional de Colombia [email protected] We evaluate the performance of various trading strategies within the context of the multi-group asset flow differential equations model. We consider scenarios in which strate- CP27 gies vary continuously and slowly, and derive mathemat- Towards Understanding Mechanisms of Pain ical justification for constant rebalanced portfolio (CRP) Transmission: a Systems Theoretic Approach strategies. The CRP strategy minimizes investment risks as investor wealth is maintained when the price moves from Pain is a universal experience. Motivated by a lack of and then returns to its original value; non-CRP strategies understanding of pain mechanisms, we develop a reduced may be exploited by others resulting in a loss of wealth. low-dimensional model of the dorsal horn circuit—the first central relay of sensory inputs to the brain. We deter- Mark DeSantis mine how a cellular switch of firing patterns in dorsal horn Mathematics transmission cells—tonic, plateau, endogenous bursting— Univ of Pittsburgh contributes to a functional switch of information transfer— [email protected] faithful transmission, enhancement, or blocking of nocicep- tive information. David Swigon Department of Mathematics Pierre Sacr´e University of Pittsburgh University of Li`ege 114 DS15 Abstracts

[email protected] University of Aberdeen Scotland Sridevi Sarma [email protected] Johns Hopkins University [email protected] Claude Wischik TauRx Therapeutics Ltd [email protected] CP27 Optogenetic Stimulation of a Meso-Scale Human Bjoern Schelter Cortical Model Institute for Complex Systems and Mathematical Biology [email protected] Mesoscale models of cortical activity provide a means to study neural dynamics at the level of neuron populations, and offer a safe and economical way to test the effects and CP27 efficacy of stimulation techniques on the dynamics of the Analysis of Cholera Epidemics with Bacterial cortex. Here, we use a physiologically relevant mesoscale Growth and Spatial Movement model of the cortex, consisting of a set of stochastic, highly non-linear partial differential equations, to study In this work, we propose novel epidemic models for cholera the hypersynchronous activity of neuron populations dur- dynamics by incorporating a general formulation of bacte- ing epileptic seizures. We use optogenetic stimulation to ria growth and spatial variation. In the first part, a general- control seizures in a hyperexcited cortex, and to induce ized ODE model is presented and it is found that bacterial seizures in a normally functioning cortex. The high spa- growth contributes to the increase of the basic reproduction tial and temporal resolution this method offers makes a number. With the derived basic reproduction number, we strong case for the use of optogenetics in treating epilep- analyze the local and global dynamics of the model. Par- tic seizures. We use bifurcation analysis to investigate the ticularly, we give a rigorous proof on the endemic global effect of optogenetic stimulation in the meso scale model, stability by employing the geometric approach. In the sec- and its efficacy in suppressing the non-linear dynamics of ond part, we extend the ODE model to a PDE model with seizures. the inclusion of diffusion to capture the movement of hu- man hosts and bacteria in a heterogeneous environment. Prashanth Selvaraj The disease threshold of this PDE model is studied again University of California, Berkeley by using the basic reproduction number. The results on [email protected] the threshold dynamics of the ODE and PDE models are compared, and verified through numerical simulation. Andrew J. Szeri University of California at Berkeley Xueying Wang Department of Mechanical Engineering Washington State University [email protected] [email protected]

James W. Sleigh CP27 University of Auckland Waikato Clinical School Benefits of Noise in Synaptic Vesicle Release [email protected] Noise is not only a source of disturbance but can also be beneficial for neuronal information processing. The release HeidiE.Kirsch of neurotransmitter vesicles in synapses is an unreliable UC San Francisco process, especially in the central nervous system. Here we [email protected] study the effect of the probabilistic nature of this process and show that how stochasticity in vesicle docking and re- lease can be beneficial for synaptic transmission. CP27 Assessing the Strength of Directed Influences Calvin Zhang, Charles S. Peskin Among Neural Signals Courant Institute of Mathematical Sciences New York University Inferring Granger-causal interactions between processes [email protected], [email protected] promises deeper insights into mechanisms underlying net- work phenomena, e.g. in the neurosciences where the level of connectivity in neural networks is of particular interest. CP27 Renormalized partial directed coherence can be used to in- Growth Dynamics for Pomacea Maculata vestigate Granger causality in such multivariate systems. A major challenge in estimating respective coherences is a Pomacea maculata is a relatively new invasive species to the reliable parameter estimation of vector autoregressive pro- Gulf Coast region and potentially threatens local agricul- cesses. We discuss improvements of the estimation pro- ture (rice) and ecosystems (aquatic vegetation). The pop- cedure that are particularly relevant in the neurosciences. ulation dynamics of Pomacea maculata have largely been un-quantified. We directly measured the growth rates of in- dividually marked snails grown in a common tank to quan- Linda Sommerlade tify their growth patterns. However, due to large intra- and Freiburg Center for Data Analysis and Modeling inter- individual variability and sample size, we were not University of Freiburg able to get statistically rigorous estimates (i.e., tight confi- [email protected] dence intervals) on overall growth dynamics. However, we were able to use a model comparison statistic to determine Marco Thiel that there are distinct growth stages. Further, these data DS15 Abstracts 115

strongly suggest that male and female growth dynamics, Infected Individuals size distributions, and overall weights, are notably different with females being generally larger. We performed simu- Initiating anti-HIV treatment during ongoing TB treat- lation studies based on observed variability, and are using ment for HIV-TB co-infected individuals has advantages these models to design additional lab experiments and field and disadvantages. Here, we develop a dynamical system studies. (system of ODEs) that helps identify an ideal treatment strategy for HIV-TB co-infected individuals. Using our Lihong Zhao model, we formulate and analyze an optimal control prob- University of Louisiana at Lafayette, Mathematics lem in order to determine a HIV-TB treatment protocol Department that provides a minimum cumulative burden from this co- [email protected] infection.

Karyn L. Sutton Abhishek Mallela University of Louisiana University of Missouri-Kansas City Lafayette [email protected] [email protected] Suzanne M. Lenhart Jacoby Carter University of Tennessee USGS National Wetlands Research Center Department of Mathematics [email protected] [email protected]

Naveen K. Vaidya CP28 Dept of Maths & Stats, University of Missouri - Kansas Optimal Control of Building’s Hvac System with City on-Site Energy Storage and Generation System Kansas City, Missouri, USA [email protected] Commercial and residential buildings consume more than 40% of the total energy in most countries, and HVAC (Heating Ventilation and Air Conditioning) systems typ- CP28 ically consume more than 50% of the building energy con- sumption. A recent study indicates that optimal control Towards a Structural Theory of Controllability of of HVAC system can achieve energy savings of up to 45%. Binary Networks Therefore, optimized control of HVAC system can poten- tially reduce significant amount of energy consumption of Almost all complex networks satisfy structural controlla- buildings. In this work, we describe a model predicted con- bility theory except for some special networks which form trol (MPC) framework that optimally computes the control a set of Lesbesgue measure zero. A important class of net- profiles of the HVAC system considering the dynamic de- works is binary networks,thatisnetworksforwhichallof mand response signal, on-site storage of electricity, on-site the existing connections have the same associated weight. generation of electricity, greenhouse gas emission as well as However, these networks often do not satisfy structural occupants comfort. The approach would determine how to controllability theory. We focus on this class of networks power the HVAC system from the optimal combination of and propose some graphical tools that can be used to char- grid electricity, on-site stored electricity and on-site gener- acterize the structural controllability of binary networks. ated electricity. Afroza Shirin Raya Horesh Graduate Stedents IBM T.J. Watson Research Center Department of Mechanical Engineering, University of [email protected] New Mexi [email protected] Young M. Lee IBM T.J. Watson Reseach Center [email protected] CP29 Stripe to Spot Transition in a Plant Root Hair Ini- Leo Liberti tiation Model IBM LIX, Ecole Polytechnique, Palaiseau, France A generalised Schnakenberg system with source and loss [email protected] terms and a spatially dependent coefficient of the nonlin- ear term is studied in 2D. The system captures active and Young Tae Chae inactive forms of the kinetics of a small G-protein ROP, Hyundai Engineering & Construction Co., Ltd which are catalysed by a gradient of the plant hormone Research and Development Division , Seoul, Republic of auxin. Localised stripe-like solutions of active ROP oc- Korea cur for high enough total auxin concentration and lie on a [email protected] complex bifurcation diagram of single and multi-pulse so- lutions. Transverse stability computations show that these Rui Zhang 1D solutions typically undergo a transverse instability into IBM T.J. Watson Reseach Center spots. The spots so formed typically drift and undergo [email protected] secondary instabilities such as spot replication. A 2D nu- merical continuation analysis is performed that shows the various stable hybrid spot-like states can coexist. Upon CP28 describing the dispersion relation of a certain non-local Optimal Treatment Strategies for HIV-TB Co- eigenvalue problem, the parameter values studied lead to 116 DS15 Abstracts

an analytical explanation of the initial instability. mial mixing rates ∼ t−2. In the end, I will show that sim- ilar slow (polynomial) mixing rates appear in many other Victor F. Brena-Medina microscopic heat conduction models. University of Bristol [email protected] Yao Li Courant Institute of Mathematical Sciences, Daniele Avitabile New York University School of Mathematical Sciences [email protected] University of Nottingham [email protected] MS1 Alan R. Champneys Nonlinearity Saturation as a Singular Perturbation University of Bristol of the Nonlinear Schr¨odinger Equation [email protected] Saturation of a Kerr-type nonlinearity in the generalized nonlinear Schr¨odinger equation (NLS) can be regarded as Michael Ward a singular perturbation which regularizes the well known Department of Mathematics blow-up phenomenon in the cubic NLS. An asymptotic ex- University of British Columbia pansion is proposed which takes into account multiple scale [email protected] behavior both in the longitudinal and transverse directions. We find that interaction of a solitary wave and an adja- cent wave field is governed by behavior of eigenfunctions CP29 of the linearized fast-scale operator. In one dimension, the Symmetry Groups and Dynamics of Time- solitary wave acts solely to reflect impinging waves and Fractional Diffusion Equation accelerates by an elastic transfer of momentum. In two dimensions, the solitary wave can be made transparent to In science and engineering the processes in which both spa- the ambient field for a certian value of wave power. This tial and temporal variations occur are often known as dif- is joint work with Jordan Allen-Flowers. fusion. Mostly diffusion process is anomalous due to the heterogeneous nature of medium therefore it can be best Karl Glasner described in terms of fractional derivatives. We propose The University of Arizona a new approach to construct the symmetry groups of frac- Department of Mathematics tional diffusion equation and using these groups we provide [email protected] some interesting physical interpretation to understand the dynamics of anomalous diffusion. MS1 Muhammad D. Khan Dark-Bright, Dark-Dark, Vortex-Bright and Other Institute of Business Management Multi-Component NLS Beasts: Theory and Recent [email protected] Applications

Motivated by recent work in nonlinear optics, as well as CP29 in Bose-Einstein condensate mixtures, we will explore a Onset of Singularities in the Pattern of Fluctua- series of nonlinear states that arise in such systems. We tional Paths of a Nonequilibrium System will start from a single dark-bright solitary wave, and then expand our considerations to multiple such waves, their A generic feature of systems away from thermal equilib- spectral properties, nonlinear interactions and experimen- rium is the occurrence of singularities in the patterns of tal observations. A twist will be to consider the dark most probable trajectories followed in rare fluctuations to solitons as effective potentials that will trap the bright remote states in phase space. We study how the singu- ones, an approach that will also prove useful in charac- larities emerge as the system is driven away from thermal terizing the bifurcations and instabilities of the system. equilibrium by an increasingly strong perturbation. We Beating, so-called dark-dark soliton variants of such states find where there is a threshold in the perturbation strength will be touched upon. Generalizations of all these notions and the scaling of the singularity location if there is no in higher dimensions and, so-called, vortex-bright solitons threshold. will also be offered. Oleg B. Kogan Panayotis Kevrekidis Cornell University University of Massachusetts [email protected] [email protected]

Mark I. Dykman Department of Physics and Astronomy MS1 Michigan State University Bifurcation and Competitive Evolution of Network [email protected] Morphologies in the Strong Functionalized Cahn- Hilliard Equation CP29 The Functionalized Cahn Hilliard (FCH) is a higher-order Polynomial Mixing Rates of Particle Systems free energy for blends of amphiphillic polymers and solvent which balances solvation energy of ionic groups against In this talk I will present our results on polynomial mixing elastic energy of the underlying polymer backbone. Its rates of some particle systems that are derived from the gradient flows describe the formation of solvent network study of microscopic heat conduction. We rigorously prove structures which are essential to ionic conduction in poly- that an energy dependent Kac-type model admits polyno- mer membranes. The FCH possesses stable, coexisting DS15 Abstracts 117

network morphologies and we characterize their geometric [email protected] evolution, bifurcation and competition through a center- stable manifold reduction which encompasses a broad class of coexisting network morphologies. The stability of the MS2 different networks is characterized by the meandering and Gene Network Models Including mRNA and Pro- pearling modes associated to the linearized system. For tein Dynamics the H −1 gradient flow of the FCH energy, using func- tional analysis and asymptotic methods, we drive a sharp- Qualitative models of gene regulatory networks have gener- interface geometric motion which couples the flow of co- ally considered transcription factors to regulate directly the dimension 1 and 2 network morphologies, through the far- expression of other transcription factors, without any inter- field chemical potential. In particular, we derive expres- mediate variables. In fact, gene expression always involves sions for the pearling and meander eigenvalues for a class transcription, which produces mRNA molecules, followed of far-from-self-intersection co-dimension 1 and 2 networks, by translation, which produces protein molecules, which and show that the linearization is uniformly elliptic off of can then act as transcription factors for other genes. Sup- the associated center stable space. pressing these multiple steps implicitly assumes that the qualitative behaviour does not depend on them. Here we Noa Kraitzman explore a class of expanded models that explicitly includes Michigan State University both transcription and translation, keeping track of both [email protected] mRNA and protein concentrations. We mainly deal with regulation functions that are steep sigmoids or step func- tions, as is often done in protein-only models. Our results MS1 thus show that including mRNA as a variable may change the behavior of solutions. Nonlinear Stability of Source Defects Roderick Edwards Defects are interfaces that mediate between two wave University of Victoria trains. Of particular interest in applications are sources Canada for which the group velocities of the wave trains to either [email protected] side of the defect point away from the interface. While sources are ubiquitous in experiments, their stability anal- ysis presents many challenges. In this talk, I will discuss MS2 nonlinear-stability results for sources that rely on pointwise Database for Switching Networks As a Tool for estimates. Study of Gene Networks

Bjorn Sandstede Continuous time Boolean networks, or switching networks, Division of Applied Mathematics represent an attractive platform for qualitative studies of Brown University gene regulation, since the dynamics at fixed parameters is bjorn [email protected] relatively easily to compute. However, it is quite difficult to analytically understand how changes of parameters af- fect dynamics. Database for Dynamics is an excellent tool MS2 for studying these models, as it rigorously approximates global dynamics over a parameter space. The results ob- Dynamics of Autonomous Boolean Networks tained by this method provably capture the dynamics a predetermined spatial scale. We combine these two ap- Autonomous Boolean networks are known to display com- proaches to present a method to study switching networks plex dynamics, originating from the absence of an external over a parameter spaces. We apply our method to experi- clock, internal time delays and the non-ideal behaviour of mental data for cell cycle dynamics. the logic gates. We study experimentally such networks on a field-programmable gate array (FPGA). In particular, Tomas Gedeon we show that networks consisting of only a few logic ele- Montana State University ments can produce long transients. We demonstrate how Dept of Mathematical Sciences these transients can be used to successfully perform reser- [email protected] voir computing, a new machine learning paradigm.

Otti D’Huys, Nicholas D. Haynes MS2 Department of Physics, Duke University Evolution of Gene Networks [email protected], [email protected] Genetic activity is partially regulated by a complicated Miguel C. Soriano network of proteins called transcription factors. An out- IFISC (UIB-CSIC) standing scientific puzzle is to understand how this genetic Campus Universitat de les Illes Balears, Palma de network can evolve. I discuss evolution of dynamics in sim- Mallorca plified models of genetic networks. By changing the logical miguel@ifisc.uib-csic.es structure randomly, it is possible to evolve the networks in an effort to identify networks that display rare dynamics - e.g. networks with long stable cycles or with a high level Ingo Fischer of topological entropy. In the context of the models, it is Campus Universitat de les Illes Balears possible to estimate optimal mutation rates. The theoreti- IFISC (UIB-CSIC) cal models pose the problem of how evolution can robustly ingo@ifisc.uib-csic.es take place in organisms. Daniel J. Gauthier Leon Glass Department of Physics, Duke University McGill University 118 DS15 Abstracts

Department of Physiology show that Eulerian quantities are not invariant subject to [email protected] arbitrary frame translation and rotation. We show in this talk scalar dispersion and residence time statistics based on Lagrangian partitions, where new scaling law behaviors MS3 are identified. Controlling Long-Term Spatial Distributions of Autonomous Vehicles in Stochastic Flow Environ- Wenbo Tang, Phillip Walker ments Arizona State University [email protected], [email protected] We present a control strategy for aquatic vessels that lever- ages the environmental dynamics and noise to efficiently navigate in a stochastic fluidic environment using the the- MS3 ory of large fluctuations. We show that a vehicle’s like- Controlled Lagrangian Prediction Using An En- lihood of transition between regions in the flow can be semble of Flow Models manipulated by the proposed control strategy, resulting in efficient navigation from one region to another. We then The technique of controlled Lagrangian prediction (CLP) experimentally verify the strategy in a fluid environment is developed to employ an ensemble of flow modes to pro- using autonomous vehicles. vide odometry-like localization information for underwater vehicles. CLP can then be fused with other underwater Christoffer R. Heckman localization technology to enable simultaneous localization U.S. Naval Research Laboratory and map-making (SLAM). Map-making functionality will [email protected] be performed to update each flow model with the latest sensor information and to decide the best flow model to Ani Hsieh use that gives the minimum localization error at any given Drexel University time. [email protected] Fumin Zhang School of Electrical and Computer Engineering Ira B. Schwartz Georgia Institute of Technology Naval Research Laboratory [email protected] Nonlinear Dynamical Systems Section [email protected] MS4 MS3 Constrained Motion of Point Vortices Interacting Dynamically with Rigid Bodies in Ideal Flow Tracking of Geophysical Flows by Robot Teams: An Experimental Approach The equations of motion for the dynamic interaction of rigid bodies and point vortices in ideal flow were only re- This talk presents our group’s recent efforts in using teams cently derived, in 2002 by Shashikanth et al and in 2003 of robots to track geophysical fluid features like Lagrangian by Borisov et al. We compare these equations with those Coherent Structures. The talk will focus on our develop- obtained by a suitable application of Diracs method of con- ment of the multi-robot Coherent Structure Testbed a straints to the N-vortex problem. In 2008, Vankerschaver novel multi-robot experimental testbed capable of creating et al derived the unconstrained equations through symplec- ocean-life flows in a laboratory setting. I will show ex- tic reduction, but several assumptions were made in the perimental results of various single vehicle and multi-robot analysis. We investigate the possibility of relaxing some of control strategies for tracking different fluidic features in a these assumptions. flow field and navigating in stochastic flows. Michael Fairchild, Scott Kelly Ani Hsieh, Dhanushka Kularatne, Dennis Larkin UNC Charlotte Drexel University [email protected], [email protected] [email protected], [email protected], [email protected] MS4 Eric Forgoston The Poincare-Hopf Theorem in Nonholonomic Me- Montclair State University chanics Department of Mathematical Sciences [email protected] This talk discusses using the Poincare-Hopf theorem and the technique of Hamiltonization as a means to study Philip Yecko the integrability nonholonomic mechanical systems (briefly, Cooper Union mechanical systems subject to non-integrable velocity con- [email protected] straints). We will focus primarily on a generalized Klebsh- Tisserand case of the Suslov problem, and use the afore- mentioned approach to determine the topology of the (two- MS3 dimensional) invariant manifolds, and in particular their Conditional Statistics with Lagrangian Coherent genus. The results will be contrasted with those expected Structures of Hamiltonian systems. Coherent structures are ubiquitous in the environment. In Oscar Fernandez order to analyze mixing and transport processes, condi- Wellesley College tional statistics are typically generated and scaling laws are [email protected] identified. Classically, these are based on flow domain par- titions from Eulerian quantities. However, recent studies Anthony M. Bloch DS15 Abstracts 119

University of Michigan [email protected] Department of Mathematics [email protected] MS5 Dmitry Zenkov Combined Effects of Connectivity and Inhibition in North Carolina State University a Model of Breathing Rhythmogenesis Department of Mathematics [email protected] The pre-Btzinger complex is an area in the brainstem which generates the breathing rhythm, an essential function for life. We model this area with realistic bursting neurons MS4 coupled in a large sparse network. We study how syn- chronous activity of the population changes due to (1) the Discretization of Hamiltonian Incompressible Flu- number of connections each cell receives (2) the fraction of ids cells which are inhibitory, and (3) the strength of excitatory and inhibitory synapses. The model is compared to exper- The geometry of incompressible, inviscid fluids can be imental data. We also ask, how do multiple phases of ac- described by Arnold’s classic formulation in terms of tivity arise? Can they arise spontaneously in unstructured geodesics on the Lie group of volume-preserving diffeo- networks, or do they require more structured networks like morphisms. In recent years this formulation has been dis- block models? cretized for computational purposes, creating a geomet- ricnumerical method that obeys a discretized version of Kameron D. Harris Kelvin’s circulation theorem. This talk will present an ex- Applied Mathematics tension of this discretization into the corresponding Hamil- University of Washington tonian view of incompressible inviscid fluids, thereby giving [email protected] a method based on the vorticity equation. Along the way we will discuss the general principles of this style of dis- Tatiana Dashevskiy cretization, which involves approximating the Lie group of Center for Integrative Brain Research volume-preserving diffeomorphisms by a finite-dimensional Seattle Children’s Research Institute Lie-group and then localizing the resulting equations by [email protected] means of a non-holonomic constraint. Eric Shea-Brown Gemma Mason Department of Applied Mathematics CMS dept. University of Washington Caltech [email protected] [email protected] Jan-Marino Ramirez Christian Lessig Center for Integrative Brain Research Technishe Universitat Berlin University of Washington [email protected] [email protected]

Mathieu Desbrun MS5 Dept. of Computing & Mathematical Sciences CALTECH A Complex Networks Approach to Malaria’s Ge- [email protected] netic Recombination Dynamics Malaria parasites evade immune systems by sequentially expressing diverse proteins on the surface of infected red MS4 blood cells. These camouflage proteins come from rapid The Lie-Dirac Reduction for Nonholonomic Sys- genetic recombination that shuffles the genes that encode tems on Semidirect Products the proteins. Because this shuffling precludes the use of traditional sequence analysis techniques, we take a new approach by mapping sequences to a network in which We consider Dirac systems with symmetry for nonholo- each vertex represents a single sequence and constraints nomic mechanical systems on Lie groups with broken sym- on recombination reveal themselves in the networks com- metry. We show reduction of Lagrange-Dirac systems and munity structure. We validate this approach on synthetic Dirac-Hamilton systems in the context of Lie-Dirac re- sequences. Application of this technique to a large set of se- duction with advected parameters. Then, we develop im- quences from both human- and ape-infecting malaria para- plicit Euler-Poincare-Suslov and Lie-Poisson-Suslov equa- sites reveals that the observed genetic states of six distinct tions with advected parameters with some illustrative ex- malaria species have arisen due to recombining and evolv- amples such as the Chaplygins ball and the second order ing a common set of initial sequence content, dating back Rivlin-Ericksen fluids. We also discuss the Dirac reduction prior to the speciation of humans and chimpanzees from on semidirect products by stages on the Hamiltonian side. their most recent common ancestors.

Daniel B. Larremore, Caroline Buckee Hiroaki Yoshimura Center for Communicable Disease Dynamics Waseday University Harvard School of Public Health [email protected] [email protected], [email protected]

Fran¸cois Gay-Balmaz Aaron Clauset Ecole Normale Superieure de Paris University of Colorado at Boulder 120 DS15 Abstracts

Computer Science Dane Taylor [email protected] Statistical and Applied Mathematical Sciences Institute Dept of Mathematics, University of North Carolina, Chapel Hi MS5 [email protected] Not-So-Random Graphs Through Wide Motifs

This work focuses on two powerful analytical methods MS6 that can model stochastic processes on (and/or of) com- Model-Based Glucose Forecasting for Type 2 Dia- plex networks: one recasts the problem as a set of ordi- betics nary differential equations, and the other amounts to a branching process. Both methods are based on the idea of Type 2 diabetes affects 9 million Americans. While treat- breaking the network into smaller pieces—hereafter called ment is complex, two important components include quan- ”motifs”—that may be re-assembled according to specific tifying the features of glucose dynamics and forecasting rules. However, these techniques are limited to random the effect of nutrition on glucose levels. Both topics are graphs containing no cycles, except for the cycles explic- addressed in this talk. First, electronic health record data itly represented within the motifs used in their assembly. are used to identify features of glucose dynamics that cor- This is a major problem for real-world phenomenons (such relate with mortality via a regression. Second, a dual un- as cascading failures due to flows reorganization) that fun- scented Kalman filter and two mechanistic models are used damentally depend on the presence of cycles much longer to forecast glucose using real data. than what these motifs-based methods allow. In this work, I will present recent developments concerning ”wide mo- David J. Albers tifs”, which generalize both the concepts of ”motifs” and Colombia University ”tree decomposition”. By opposition to traditional motifs, Biomedical Informatics cycles may be broken into pieces to span multiple wide [email protected]. motifs, thus allowing for cycles of arbitrarily long lengths that may share intricate overlaps. This perspective can be MS6 used for a broad spectrum of networks, spanning from de- terministic structures to random graphs, thus blurring the Predicting Recovery of Consciousness in Patients line between these extremes. The approach broadens the with Brain Injury class of problems that can be approached analytically and Oscillatory electrical activity is associated with informa- introduces new challenges in the detection and characteri- tion processing in the brain. Patients with severe brain zation of network structures. Conceptual similarities with injuries often exhibit disorders of consciousness along with ”belief propagation” algorithms and the ”tensor network” disturbed oscillatory activity. This project was designed representation of entangled quantum states should allow to determine whether continuous measures of brain oscil- for these different fields to cross-fertilize. lations can be used to predict recovery of consciousness on Pierre-Andre Noel the time-scale of days. Sparse partial least squares and Department of Mechanical Engineering high-dimensional classification algorithms are used to de- University of California, Davis termine latent variables used for prediction in a novel sub- [email protected] set of patients. Hans-Peter Frey Department of Neurology, Columbia University MS5 [email protected] Causal Network Inference by Optimal Causation Entropy MS6 The abundance of time series data, which is in sharp con- Assimilating Sleep - Putting the Model to the Data trast to limited knowledge of the underlying network dy- namic processes that produce such observations, calls for Over the past four years we investigated tools for data as- a general and efficient method of causal network infer- similation and forecasting from models of the sleep-wake ence. We develop mathematical theory of Causation En- regulatory system. Ill report on the challenges we now face tropy (CSE), a model-free information-theoretic statistic as we collect data from brainstem cell groups in freely be- designed for causality inference. We prove that for a given having animals and attempting to apply these tools. node in the network, the collection of its direct causal neighbors forms the minimal set of nodes maximizing Cau- Bruce J. Gluckman sation Entropy, a result we refer to as the Optimal Causa- Penn State University tion Entropy (oCSE) Principle, for which we develop ef- [email protected] ficient algorithms. Analytical and numerical results for Gaussian processes on large random networks highlight that inference by oCSE outperforms previous leading meth- MS6 ods including Conditional Granger Causality and Transfer Time Series Modeling and Analysis Using Elec- Entropy. Interestingly, our numerical results also indicate tronic Health Record Data that the number of samples required for accurate inference depends strongly on network characteristics such as the Electronic health record data contain valuable information density of links and information diffusion rate and not on about biology and health care, but the data hold a num- the number of nodes. ber of challenges, including the fact that measurements are sparse and irregular. Furthermore, health care is a Jie Sun, Erik Bollt highly complex process that makes drawing causal conclu- Clarkson University sions very difficult. We discuss alternate time parameteri- [email protected], [email protected] zations that may lead to a more stationary time series, and DS15 Abstracts 121

we discuss the use of Granger causality to tease out causes ference of dominant neural pathways that control sensori- and confounders. motor responses is challenging since neurons are dynamical objects and interactions within the network are also dy- George Hripcsak namic. In our study, we construct a Probabilistic Graphical Department of Bioinfomatics, Columbia University Model (PGM) for the C. elegans connectome that repre- [email protected] sents the ’effective connectivity’ between the neurons (cor- relations) and takes into account the dynamics. The struc- ture of the PGM is learned using Bayesian methods capable MS7 of learning the structure of an undirected graphical model Reconstruction of Structural Connectivity in Neu- from a collection of time series. The collections are ob- ronal Networks Using Compressive Sensing of Net- tained by a systematic excitation of neurons in a recently work Dynamics developed computational dynamical model for the C. ele- gans that simulates single neural responses and interactions Taking into account the prominence of sparsity in neuronal between the neurons (synaptic and gap). Bayesian infer- connectivity, we develop a framework for efficiently re- ence methods applied to the constructed PGM allow us to constructing neuronal connections in a sparsely-connected, extract neural pathways in the connectome of C. elegans re- feed-forward network model with nonlinear dynamics. sponsible for experimentally well characterized movements Driving the network with a small ensemble of random stim- of the worm such as forward and backward locomotion. In uli, we derive a set of underdetermined linear systems relat- addition, we show that the framework allows for inference ing the network connectivity to neuronal firing rates. Via of pathways that correspond to movements that were not compressive sensing, we accurately recover sparse network fully characterized in experiments and to perform ’reverse- connectivity and also realistic network inputs distinct from engineering’ studies in which a typical setup on the mo- the training set of stimuli. tor neurons layer is imposed and dominant pathways that propagate to the sensory layer through the interneurons Victor Barranca layer are being identified. New York University [email protected] Eli Shlizeman University of Washington Douglas Zhou [email protected] Shanghai Jiao Tong University [email protected] MS7 David Cai Courant Institute for Mathematical Sciences, NYU Topology Reconstruction of Neuronal Networks Shanghai Jiao-Tong University [email protected] Current experimental techniques usually cannot probe the global interconnection pattern of a network. Thus, recon- structing or reverse- engineering the network topology of MS7 coupled nodes based upon observed data has become a very Theoretical Modeling of Neuronal Dendritic Inte- active research area. Most existing reconstruction methods gration are based on networks of oscillators with generally smooth dynamics. However, for nonlinear and non-smooth stochas- We address the question of how a neuron integrates excita- tic dynamical systems, e.g., neuronal networks, the recon- tory (E) and inhibitory (I) inputs from different dendritic struction of the full topology remains a challenge. Here, we sites. For an idealized neuron with an unbranched den- present a noninterventional reconstruction method, which drite, a conductance-based cable model is derived and its is based on Granger causality theory, for the widely used asymptotic solutions are constructed. The solutions reveal conductance-based, integrate-and-fire type neuronal net- the underlying mechanisms of a dendritic integration rule works. For this nonlinear system, we have established a discovered in a recent experiment. We then extend our direct theoretical connection between Granger causal con- analysis to the multi-branch case and confirm our analysis nectivity and structural connectivity. through numerical simulation of a realistic neuron. Douglas Zhou Songting Li, Douglas Zhou Shanghai Jiao Tong University Shanghai Jiao Tong University [email protected] [email protected], [email protected] Yanyang Xiao, Yaoyu Zhang, Zhiqin Xu David Cai Department of Mathematics and Institute of Natural New York University Sciences Courant institute Shanghai Jiao Tong University [email protected] [email protected], [email protected], [email protected] MS7 David Cai Functional Connectomics from Data: Constructing Courant Institute for Mathematical Sciences, NYU Probabilistic Graphical Models for Neuronal Net- Shanghai Jiao-Tong University works [email protected] The nervous system of the nematode Caenorhabditis el- egans (C. elegans) is comprised of 302 neurons for which MS8 electro-physical connectivity map (i.e. connectome) is fully resolved. Although the static connectome is available, in- Investigation of Boussinesq non-linear Interactions 122 DS15 Abstracts

Using Intermediate Models Jeffrey Oishi Department of Physics Nonlinear coupling among wave modes and vortical modes Farmingdale State College is dissected in order to probe the question: Can we dis- [email protected] tinguish the wave-vortical interactions largely responsible for formation versus evolution of coherent, balanced struc- tures? It is well known that the quasi-geostrophic (QG) MS8 equations can be derived from the Boussinesq system in a non-perturbative way by ignoring wave interactions and Interaction of Inertial Oscillations with a considering vortical modes only. One qualitative difference Geostrophic Flow between those two models is the lack of skewness in the QG dynamics. In this talk, non-perturbative intermediate The interaction between large horizontal scale pure iner- models that include more and more classes of non-linear tial oscillations and small horizontal scale geostrophic field interactions will be used to identify their role in different is investigated in this work. As a result of the interac- qualitative properties of the Boussinesq system. Numerical tion rapid vertically propagating near inertial waves and results will be shown to describe the effect of each class in trapped or non-propagating inertial oscillations form. The the transfer of energy between vortical modes and waves, trapped oscillations inherit smaller spatial scales from the transfer of energy (or the lack of it) between scales, forma- geostrophic field and remains in the upper ocean. The near tion of vortices and skewness. inertial waves propagate into the deep ocean within days, Gerardo Hernandez-Duenas thus allowing the inertial signal to be felt in the deep ocean. National University of Mexico, Juriquilla The study hence offers an alternate explanation for the age Institute of Mathematics old problem of vertical propagation of near inertial waves [email protected] and formation of small scale inertial oscillations in an ide- alized set up. The interaction is however non-energetic, which is consistent with previous works. Leslie Smith Mathematics and Engineering Physics University of Wisconsin, Madison Jim Thomas [email protected] New York University Courant Institute Samuel Stechmann [email protected] University of Wisconsin - Madison [email protected] Shafer Smith Center for Atmosphere Ocean Science Courant Institute MS8 [email protected] Internal Wave Generation by Convection Oliver Buhler When a convectively unstable region is adjacent to a stably Courant Institute of Mathematical Sciences stratified region, the convection can produce internal waves New York University within the stable region. This is thought to occur in stars, [email protected] gaseous planets, the Earths atmosphere, oceans and lakes, and possibly even the Earths core. We describe a model for estimating the wave generation by convection based on MS8 Lighthills theory, and compare the model to high-resolution simulations using the Dedalus code. Interactions Between Near-Inertial Waves and Tur- bulence in the Ocean Daniel Lecoanet UC Berkeley Wind forcing of the ocean generates a spectrum of inertia- Astronomy Department gravity waves that is sharply peaked near the local inertial [email protected] (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant Keaton Burns role in the slow, large-scale dynamics of the ocean. To MIT Kavli Institute for Astrophysics and Space Research analyse this role, we develop a new model of the nondissi- [email protected] pative interactions between NIWs and mean flow using a variational implementation of the generalised-Lagrangian- Geoffrey M. Vasil mean formalism. The new model couples the Young & Ben Theoretical Astrophysics Center Jelloul model of NIWs with a quasi-geostrophic model in Astronomy Department, University of California, which the relation between potential vorticity and stream- Berkeley function is modified by a quadratic wave term. The model geoff[email protected] reveals that NIWs act as an energy sink for the mean flow: NIWs forced at large scales experience a horizontal scale Eliot Quataert cascade through refraction and advection; as a result, their UC-Berkeley potential energy increases at the expense of the mean en- [email protected] ergy. The implications for ocean energetics are discussed.

Benjamin Brown LASP and Dept. Astrophysical & Planetary Sciences Jacques Vanneste University of Colorado, Boulder School of Mathematics [email protected] University of Edinburgh DS15 Abstracts 123

[email protected] [email protected]

MS9 MS9 Topological Data Analysis for and with Contagions Local Inference of Gene Regulatory Networks from on Networks Time Series Data The study of contagions on networks is central to the un- Temporal dynamics of gene expression levels may be par- derstanding of collective social processes and epidemiol- tially explained by interactions between certain proteins, ogy. When a network is constrained by an underlying called transcription factors, which act to either promote manifold such as Earth’s surface (as in most social and or repress RNA-synthesis (transcription) of specific genes. transportation networks), it is unclear how much spread- Discovering the regulatory relationships in these transcrip- ing processes on the network reflect such underlying struc- tion networks is a difficult goal of systems biology, but ture, especially when long-range edges are also present. We one which promises to greatly enhance experimental de- address the question of when contagions spread predomi- sign. In this talk, we describe a statistical approach to nantly via the spatial propagation of wavefronts (e.g., as infer the structure of gene regulatory networks from time observed for the Black Death) rather than via the appear- series data. ance of spatially-distant clusters of contagion (as observed for modern epidemics). To provide a concrete scenario, we Francis C. Motta, Kevin McGoff, Anastasia Deckard, Xin study the Watts threshold model (WTM) of social conta- Guo Guo, Tina Kelliher, Adam Leman, Steve Haase, gions on what we call noisy geometric networks, which are John Harer spatially-embedded networks that consist of both short- Duke University range and long-range edges. Our approach involves us- [email protected], mcgoff@math.duke.edu, ing multiple realizations of contagion dynamics to map the [email protected], [email protected], network nodes as a point cloud, for which we analyze the [email protected], [email protected], geometry, topology, and dimensionality. We apply such [email protected], [email protected] maps, which we call WTM maps, to both empirical and synthetic noisy geometric networks. For the example of a noisy ring lattice, our approach yields excellent agreement with a bifurcation analysis of the contagion dynamics. Im- MS9 portantly, we find for certain dynamical regimes that we Patterns in Discrete Ecological Dynamical Systems can identify the network’s underlying manifold in the point Revealed Through Persistent Homology cloud, highlighting the utility of our method as a tool for inferring low-dimensional (e.g., manifold) structure in net- Persistent homology captures information about a system works. Our work thereby finds a deep connection between regarding longevity of topological features, such as level the fields of dynamical systems and nonlinear dimension sets of a function. This provides a novel perspective when reduction. applied to discrete time dynamical systems. In particu- Dane Taylor lar, interesting patterns arise when applied to the logistic Statistical and Applied Mathematical Sciences Institute map; a common population model. This pattern will be Dept of Mathematics, University of North Carolina, discussed and extended to other systems, including contin- Chapel Hi uous systems. [email protected]

Rachel Neville Florian Klimm Colorado State University Master of Science (Physics) [email protected] Humboldt-Universit¨at, Berlin [email protected]

MS9 Heather Harrington Network Spread and Control of Invasive Species University of Oxford and Infectious Diseases [email protected]

We introduce a method for coupling vector-based trans- Miroslav Kramar portation networks (e.g. agents traveling by vehicle) onto a Rutgers University spatially continuous model of a biological epidemic. Anal- Department of mathematics ysis for plant invasions yields a unique, stable, steady-state [email protected] solution with an optimal control for the infected vectors, with network topology affecting the efficacy of the con- Konstantin Mischaikow trol. Numerical results are shown for the cheatgras invasion Department of Mathematics of Rocky Mountain National Park based on the presence Rutgers, The State University of New Jersey model of Strickland et al. 2014. [email protected]

Christopher Strickland Mason A. Porter SAMSI Statistical and Mathematical Sciences Institute University of Oxford [email protected] Oxford Centre for Industrial and Applied Mathematics [email protected] Patrick Shipman Department of Mathematics Peter J. Mucha Colorado State University University of North Carolina Chapel Hill 124 DS15 Abstracts

[email protected] Nanjing University of Aeronautics and Astronautics [email protected]

MS10 Stability Analysis of PDEs with Two Spatial Di- MS10 mensions Using Lyapunov Methods and SOS What Is Wrong with Non-Smooth Mechanics and How Memory Effects Can Fix It? In this talk we consider stability of parabolic linear partial differential equations with polynomial coefficients and two Non-smooth mechanics has many intricacies. It can pro- spatial variables. We use Sum-of-Squares, polynomial opti- vide some surprising predictions or even fail to predict mization, and the Positivstellensatz to numerically search the dynamics past certain singularities. Such singularities for quadratic inhomogeneous Lyapunov functions. Nega- where the equations break down include various forms of tivity of the derivative is enforced using a new type of slack the Painleve paradox and the two-fold singularity of fric- variable called a ”spacing function”. The technique was tional systems. This talk looks at the reasons why these tested numerically on a two-dimensional biological PDE singularities occur and addresses the issue by adding more model of population growth model and compared to the physics to the mechanical model. It turns out that finite analytic solution. wave-speed within the mechanical system is sufficient for unique predictions, which can be taken into account with Evgeny Meyer, Matthew Peet a single correction term dependent only on the wave speed Arizona State University and geometry. [email protected], [email protected] Robert Szalai University of Bristol MS10 [email protected] Differential Equations with Variable Delay and Their Connection to Partial Differential Equations MS11 Time delay systems can be described by delay differential Phase Transitions in Models for Social Dynamics equations or by a partial differential equation (PDE) with non-local boundary conditions. The domain of the PDE is Flocking models abound in the recent mathematical and equal to the state space interval of the delay system. For scientific literature. These models can be applied to or- variable delays a moving boundary appears in the PDE ganisms which exhibit collective behavior; such models are representation. Conditions for a transformation from vari- often applied to insects, fish, birds, and even to humans. I able delay (domain) to constant delay (domain) are stud- will introduce several flocking models, both deterministic ied, leading to a fundamental dichotomy of variable delay and stochastic, at the microscopic scale. I will then discuss systems with qualitatively different properties. their kinetic and hydrodynamic limits and show that phase transitions can occur on all three scales. Gunter Radons Chemnitz University of Technology Alethea Barbaro [email protected] Case Western Reserve University [email protected] Andreas Otto Institute of Physics Chemnitz University of technology MS11 [email protected] A Center Manifold and Complex Phases for a Large Number of Interacting Particles David Mueller Chemnitz University of Technology We investigate a system of ordinary differential equations [email protected] (ODEs) describing interacting particles, with applications to schools of fish. This model has many advantages over discrete systems of interacting particles and seems to cap- MS10 ture the interactions of animals better than the classical Delayed Boundary Conditions in Control of Con- discrete Czirok-Vicsek (or boids) model. The main differ- tinua ence is that in our system the animal is allowed to adjust its velocity as well as direction to that of its neighbors. This is The mechanical model of a basic problem of electroacous- the behavior observed in nature and it makes our system tics is considered. The governing PDE is the 1D wave more suitable to applications to real animals. The sys- equation with delayed boundary conditions. The system tem of ODEs can also be analyzed using methods from dy- can be transformed into a delay differential equation of namical systems and it turns out to have a two-parameter neutral type with two delays. The zero-measure regions (velocity and direction) asymptotic solution as t becomes are constructed analytically in the parameter plane of the large. It also possesses a very rich set of stationary solu- gain parameter and the ratio of the delays where the sys- tions that all are unstable. tem is exponentially stable. The physical relevance of this In this talk we discuss the center manifold of the migrat- peculiar stability chart is highlighted. ing state (attractor) and applications to simulations of an- chovies off the coast of Peru and Chile. The effects of El Gabor Stepan Nino will also discussed. Department of Applied Mechanics Budapest University of Technology and Economics Bjorn Birnir [email protected] University of California Department of Mathematics Li Zhang [email protected] DS15 Abstracts 125

Luis Bonilla systems by superposing a disturbance topology on the com- Universidad Carlos III de Madrid munication network. Within this framework, we develop G. Millan Institute of Fluid Dynamics, Nanoscience & conditions for stochastic synchronization and the rate of IndMath convergence to synchronized states. [email protected] Subhradeep Roy, Nicole Abaid Jorge Cornejo-Donoso Virginia Polytechnic Institute and State University UCSB [email protected], [email protected] Bren School [email protected] MS12 Versatile Vibrations: Partially Synchronized States MS11 in Mechanical Systems from Microns to Kilometers Modeling Earthquake Cycles on Faults Separating In this talk I’ll describe the dynamics of coupled oscil- Variable Materials lators in three systems: optomechanical microdisk res- We have developed a computational method for studying onators, mechanical metronomes, and pedestrians on sus- how the earthquake cycle is affected by heterogeneities in pension bridges. Though drastically different in origin and the material surrounding a fault. Finite difference oper- in scale, the equations of motion share many similarities. I ators satisfying a summation-by-parts rule are applied to will present analytical and numerical techniques for solving the 2D elastodynamic wave equation and weak enforce- those equations and discuss some unsolved problems and ment of boundary conditions are enforced through the open questions regarding networks of coupled oscillators. simultaneous-approximation-method. This combined ap- Daniel Abrams proach leads to a provably stable and high-order accurate Northwestern University method. Non-planar fault geometries, variable materials [email protected] and inelastic response are incorporated. As a first step we consider the bimaterial problem on planar, vertical strike slip fault. We find that rupture propagates in the pre- MS12 ferred direction and we are currently studying the long term behavior of the earthquake cycle and under what con- Wind-Induced Synchrony Causes the Instability of ditions rupture in the non-preferred direction (periodically a Bridge: When Millennium Meets Tacoma observed on natural faults) is possible. We aim at better understanding the cause of dangerous vi- Brittany Erickson brations and bridges collapsing as a result of wind-induced Portland State University oscillations at a frequency different from the natural fre- [email protected] quencies of a bridge, including the collapse of the Tacoma Narrows Bridge and a long-wave resonance vibration of the Volga Bridge. We propose a synchronization-based MS11 mechanism that can explain the shift of the resonant fre- quency due to wind-induced synchronization of suspension Mathematical Challenges in Ground State Forma- cables/load-bearing elements of a bridge. We also draw tion of Isotropic and Anisotropic Interaction parallels between wind-excitation and crowd synchrony In this talk we will present a mathematical framework for and present a bifurcational, analytically tractable model, studying ground state formation in a general class of kine- inspired by the Millennium Bridge case. matic models which are often used to understand the phys- Igor Belykh ical, biological and social world. I will first discuss the case Department of Mathematics and Statistics of when particles communicate isotropically and, time per- Georgia State University mitting, will present new developments in the mathemati- [email protected] cal theory of anisotropic pattern formation.

David T. Uminsky Russell Jeter University of San Francisco Georgia State University Department of Mathematics [email protected] [email protected] Vladimir Belykh Lobachevsky State University of Nizhny Novgorod, Russia MS12 [email protected] Synchronization over Networks Inspired by Echolo- cating Bats MS12 While number of organisms have made use of active sen- Network Graph Can Promote Faster Consensus sory systems, bats are particularly effective at echoloca- Reach Despite Large Inter-Agent Delays tion, wherein they emit ultrasonic waves and sense echoes to navigate their environment. One of the greatest chal- This presentation stems from the authors work on the inter- lenges of echolocating in a group is jamming, which oc- play between delays, graphs, and dynamical systems. Here, curs when echoes from an individuals calls become diffi- we consider a class of widely-studied linear consensus prob- cult to distinguish from those of its peers. Nevertheless, lem with inter-agent communication delays. For this class bats are observed to avoid the negative effects of jamming of systems, it is known that consensus is guaranteed only if in behavioral experiments. Drawing inspiration from this the inter-agent delay is less than a certain margin, known phenomenon, we incorporate the effect of jamming into a as the delay margin. We investigate how delays and the classical model of synchronization among coupled dynamic arising graph formed by agent connectivity can influence 126 DS15 Abstracts

the speed of reach of agents to consensus. Since the solu- [email protected] tion to this problem is analytically intractable, simulation studies with randomization are systematically performed Karna V. Gowda to investigate it. The three non-trivial findings are as fol- Northwestern University lows: (i) for large inter-agent delays less than the delay [email protected] margin, there exist some particular graphs that promote considerably faster reach of agents to consensus, (ii) for a given graph, consensus in the presence of larger delays can MS13 be reached faster if inter-agent couplings are weaker but Fluctuating Hydrodynamics of Microparticles in not stronger, (iii) for small size networks, there seems to Viscoelastic Fluids be a way to decide which inter-agent links to remove in order for the agents to reach consensus faster. These pre- Abstract not available. liminary results call for further research in the pursuit of revealing the most immune graphs that also promote large Scott McKinley decay rate in system states of various dynamical systems, University of Florida against the detrimental effects of delays. scott.mckinley@ufl.edu Min Hyong Koh Northeastern University [email protected] MS13 Low-Damping Transition Times in a Ferromagnetic Rifat Sipahi Model System Department of Mechanical and Industrial Engineering Northeastern University Abstract not available. [email protected] Katherine Newhall Courant Institute of Mathematical Science MS13 New York University Stochastic Boundary Conditions for Molecular Dy- [email protected] namics: From Crystal to Melt

Motivated by the need for closure relations in continuum- MS14 atomistic simulations, we develop non-periodic molecular Topological Detection of Structure in Neural Ac- dynamic boundary conditions with consistent dynamics to tivity Recordings traditional NPT algorithms. A hypothesized stochastic model is employed at the boundary and parameters are In biology, observations are often related to variables of fit on the fly via statistical sampling of the interior. Such interest through unknown monotonic nonlinearities. De- a method allows us to examine non-traditional computa- tecting structure in the presence of such nonlinearities can tional domains that allow us to focus on interfaces while be challenging, as eigenvalue-based methods are often mis- accounting for local curvatures. leading. However, algebro-topological tools can provide measurements robust to such transformations, allowing the Gregory J. Herschlag detection of the presence or absence of intrinsic structure. Department of Mathematics To demonstrate, we detect the geometric structure arising Duke University from hippocampal place cells directly from neural record- [email protected] ings.

Sorin Mitran Chad Giusti University of North Carolina Chapel Hill Warren Center for Network and Data Sciences [email protected] University of Pennsylvania [email protected]

MS13 Carina Curto, Vladimir Itskov Tipping and Warning Signs for Patterns and Prop- Pennsylvania State University agation Failure in SPDEs [email protected], [email protected] In this talk, I shall report on recent results regarding early- warning signs for pattern formation in stochastic partial MS14 differential equations. In particular, it will be shown that classical scaling laws from stochastic ordinary differential An Algebro-Topological Perspective on Hierarchi- equations can be carried over to the SPDE case. This cal Modularity of Networks is illustrated in the context of the Swift-Hohenberg equa- tion, analytically and numerically. Furthermore, I shall (Joint work with R. Levi and S. Raynor) Recent research discuss numerical results for warning signs for the stochas- by, among others, Bassett and her collaborators, has shown tic Fisher-KPP equation in the case of noisy invasion front that brain networks exhibit hierarchical modularity, which traveling waves near positive absorption probability events varies with time during learning. In this talk I will describe leading to propagation failure. Several interesting potential work on applying methods from algebraic topology in an future directions for dynamical systems analysis of SPDEs attempt to characterize and classify those hierarchically will also be sketched. modular graphs that arise as brain networks.

Christian Kuehn Kathryn Hess Vienna University of Technology Ecole´ Polytechnique Federale De Lausanne DS15 Abstracts 127

kathryn.hess@epfl.ch [email protected], [email protected]

MS14 MS15 The Topology of Fragile X Syndrome Reconstructing Dynamics of Unmodeled Variables Assimilation of data with models of physical processes is Fragile X syndrome (FXS) is the most common known a crucial component of modern scientific analysis. In re- inherited cause of developmental disability and the most cent years, nonlinear versions of Kalman filtering have been common single-gene risk factor for autism. In this talk I developed, in addition to methods that estimate model pa- will give a brief description of the algorithm used by Map- rameters in parallel with the system state. We propose a per/Iris to produce a Reeb-like graph representation from a substantial extension of these tools to deal with the specific dataset, and then describe how its application to MRI data case of unmodeled variables, when training data from the has led to the potential identification of higher and lower variable is available. The method uses a stack of several, functioning subgroups within a population of children with nonidentical copies of a physical model to jointly recon- FXS. struct the variable in question. We demonstrate the ability of this technique to accurately recover an unmodeled ex- David Romano perimental quantity, such as an ion concentration, from a Stanford School of Medicine single voltage trace after the training period is completed. [email protected] The method is applied to reconstruct the potassium con- centration in a neural culture from multielectrode array voltage measurements. MS14 The Neural Ring: Using Algebraic Geometry to Franz Hamilton Analyze Neural Codes George Mason University [email protected] Neurons represent external stimuli via neural codes, and the brain infers properties of a stimulus space using only Timothy Sauer the intrinsic structure of the neural code. We define the Department of Mathematical Sciences neural ring, an algebraic object that encodes the combina- George Mason University torial data of a neural code. Neural rings can be expressed [email protected] in a ‘canonical form’ that translates to a minimal descrip- tion of code’s structure. This provides information about structure in the stimulus space, and how changing the code MS15 affects these properties. Intramural Forecasting of Cardiac Dynamics Using Data Assimilation Nora Youngs Department of Mathematics As a first step in reconstructing the three-dimensional Harvey Mudd College propagation and breakup of electrical waves, a data- [email protected] assimilation system is coupled to a simple model of car- diac electrical dynamics. Data assimilation is a technique common in numerical weather prediction for combining ob- MS15 servations with a numerical model to derive an improved estimate of the state of a dynamical system. Here an en- Modeling Excitable Dynamics of Cardiac Cells semble Kalman filter is used on synthetic data for both 1D and 3D models. In the past decades many mathematical models of differ- ent complexity have been devised describing the excitable Matthew J. Hoffman dynamics of cardiomyocytes and cardiac tissue. To assess Rochester Institute of Technology these models their ability to predict experimental cardiac [email protected] dynamics has to be probed. The model evaluation can be performed in a data assimilation frame work where the Elizabeth M. Cherry model is driven by measured data and after some tran- Rochester Institute of Technology sient time the input is switched off and the output of the School of Mathematical Sciences free running model is compared to the true evolution of [email protected] the experimental system. To assess the fidelity of selected models we employ different state and parameter estimation algorithms, and apply them to experimental data. MS15 Sebastian Berg Tracking Neuronal Dynamics During Seizures and Alzheimer’s Disease Max Planck Institute for Dynamics and Self-Organization Research Group Biomedical Physics Observability of a dynamical system requires an under- [email protected] standing of its statethe collective values of its variables. However, existing techniques are too limited to measure T.K. Shajahan, Jan Schumann-Bischoff all but a small fraction of the physical variables and pa- Max Planck Institute for Dynamics and Self-Organization rameters of neuronal networks. We constructed models of [email protected], jan.schumann-bischoff@ds.mpg.de the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them Ulrich Parlitz, Stefan Luther into a model-based framework from modern control the- Max Planck Institute for Dynamics and Self-Organization ory. We demonstrated the meaningful estimation of the Research Group Biomedical Physics dynamics of small neuronal networks using as few as a sin- 128 DS15 Abstracts

gle measured variable. Specifically, we assimilated noisy brings new clues to understand this puzzling phenomenon membrane potential measurements from individual hip- and optimize human travel and information flow. pocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and Zoltan Neda the activities of different neuronal types during seizures. Babes-Bolyai University We used reconstruction to account for unmeasured parts Department of Physics of the neuronal system, relating micro-domain metabolic [email protected] processes to cellular excitability, and validate the recon- struction of cellular dynamical interactions against actual Geza Toth measurements. Recently, we applied the method to intra- Hungarian Central Statistical Office cellular Ca2+ dynamics using cytoplasmic Ca2+ as an ob- [email protected] servable to reconstruct and identify the differences between mitochondrial bioenergetics in control and Alzheimers dis- Andras Kovacs ease states. Edutus College Department of International Business Ghanim Ullah [email protected] University of South Florida [email protected] Istvan Papp, Levente Varga Babes-Bolyai University MS16 Department of Physics [email protected], [email protected] Feasibility of Micro-Grid Adoptions in Spatially- Embedded Urban Networks MS16 We present a data-driven citywide simulation scheme that combines heterogeneous demand with a complex systems The Brain in Space approach. We present micro grid simulations via DC power Based on experimental evidence here we argue that com- flow dynamics combined with real (photovoltaic) PV gener- puting in the brain is based on deeply physical principles ation and demand profiles of individual buildings in a city, in which form follows function: although there is a com- modeled after high temporal-resolution smart-grid data. plex network of computing elements, this network is not We explore the efficiency of spatial networks at three dif- an abstract graph, but a physical network embedded both ferent scales from individual buildings to micro-grid neigh- in space and time and these physical properties are just borhoods to an entire city. as much part of information processing in the brain as the Marta Gonzalez signals themselves that are being transmitted through the Civil and Environmental Engineering network. MIT Zoltan Toroczkai [email protected] University of Notre-Dame [email protected] MS16 Maria Ercsey-Ravasz Cascading Failures and Stochastic Methods for Faculty of Physics Mitigation in Spatially-Embedded Random Net- Babes-Bolyai University, Romania works [email protected] We have demonstrated that cascading failures are non-self- averaging in spatial graphs, hence predictability is poor Kenneth Knoblauch, Henry Kennedy and conventional mitigation strategies are largely ineffec- Stem cell and Brain Research Institute, INSERM U846 tive. In particular, we have shown that protecting all nodes Bron, France (or edges) by the same additional capacity (tolerance) can [email protected], [email protected] actually lead to larger global failures, i.e., ”paying more can result in less”, in terms of robustness. Here, we explore stochastic methods for optimal distribution of resources MS17 (capacities) subject to a fixed total cost. On the Role of Stochastic Delays in Gene Regula- tory Networks Gyorgy Korniss Department of Physics, RPI In gene regulatory networks delays emerge from sequen- [email protected] tial assembly and accumulation of macromolecules. Fur- thermore, the stochastic nature of biochemical processes leads to stochastic variations in the delay. This may lead MS16 to counter intuitive dynamics where increasing uncertainty Spatial Distribution of Population and Scaling in can increase the robustness of the system. In this talk we Human Travel present novel methods that allow us to evaluate the exact stability of equilibria in systems with stochastic delays. We An interesting scaling law connecting the travel time and demonstrate these tools on an auto-regulatory network. distance was recently observed in human traveling modes and information spreading. Further we go, faster we do Marcella Gomez, Matthew Bennett that. Seemingly the spatial distribution of population and Rice University the presence of hubs are responsible for this very general [email protected], [email protected] phenomenon. Investigating the connection between pop- ulation density distribution and the mean traveling speed Richard Murray DS15 Abstracts 129

Control and Dynamical Systems [email protected] California Institute of Technology [email protected] Jeff Hasty Department of Bioengineering University of California, San Diego MS17 [email protected] New Mechanisms for Patterns, Transitions, and Coherence Resonance for Systems with Delayed Lev S. Tsimring Feedback University of California, San Diego [email protected] Controlling patterns via delayed feedback is an efficient means of pattern resilience. Computations demonstrate complex dynamics for PDE’s with Pyragas control. We give a new analysis for stochastic PDE’s with delay, cap- MS18 turing novel spatio-temporal pattern mechanisms in the Homoclinic Snaking Near a Codimension-two Swift-Hohenberg equation (SHE) with Pyragas control, not Turing-Hopf Bifurcation Point observed for the standard SHE. We show that traveling waves appear via coherence resonance-type phenomena and Spatiotemporal Turing-Hopf pinning solutions near a codi- compare these to other multimode patterns generated by mension two Turing-Hopf point are studied. Both the delays. Turing and Hopf bifurcations are supercritical and sta- ble. The pinning solutions exhibit coexistence of stationary Rachel Kuske stripes of near critical wavelength and time periodic oscilla- University of British Columbia tions near the characteristic Hopf frequency. The solution [email protected] branches are organized in a series of saddle-node bifurca- tions similar to snaking structures of stationary pinning so- Chia Lee lutions. Time dependent depinning dynamics outside the UBC Mathematics saddle-nodes are illustrated. Wavelength variation within [email protected] the snaking region is discussed, and reasons for the varia- tion are given in the context of amplitude equations. The Vivi Rottschaefer pinning region is compared favorably to the Maxwell line Mathematical Institute found numerically by time evolving the amplitude equa- Leiden University tions [email protected] Justin C. Tzou Dalhousie University MS17 [email protected] Dynamics with Stochastically Delayed Feedback: Designing Connected Vehicle Systems Yiping Ma Department of Applied Mathematics In this talk we present novel mathematical tools that allow University of Colorado, Boulder one to evaluate the dynamics of systems where stochactic- [email protected] ity appears in the feedback delay. In particular we analyze the mean and second moment dynamics in order to evalu- Alvin Bayliss ate absolute and convective instabilities in networked sys- Northwestern University tem. We apply these methods to networks of vehicles that [email protected] exchange information via vehicle-to-vehicle (V2V) commu- nication. In such systems stochastic delays appear due to intermittencies and packet loss. Bernard J Matkowsky Department of Engineering Sciences and Applied Gabor Orosz, Wubing Qin Mathematics University of Michigan, Ann Arbor Northwestern University Department of Mechanical Engineering [email protected] [email protected], [email protected] Vladimir A. Volpert Northwestern University MS17 [email protected] Synchronization of Degrade-and-Fire Oscillations Via a Common Activator MS18 In this talk, we examine an experimentally motivated stochastic model for coupled degrade-and-fire gene oscil- Localised Solutions in a Non-Conservative Cell Po- lators, where a core delayed negative feedback establishes larization Model oscillations within each cell, and a shared delayed positive feedback couples all cells. We use analytic and numeri- We study a reaction-diffusion model for cell polarization, cal techniques to investigate conditions for one cluster and which exhibits pinned front solutions as a consequence of multi-cluster synchrony. A nonzero delay in the shared mass conservation. When a source and a sink term are positive feedback, as expected for experimental systems, is added to the model, the front solutions vanish. This gives found to be important for synchrony to occur. rise to spike solutions and the snaking scenario. Using numerical and analytical tools, we characterize these be- William H. Mather haviours. Finally we investigate the connection between Virginia Tech Physics the snaking and front solutions, when the non-conservative 130 DS15 Abstracts

terms tend to zero. Edgar Knobloch University of California at Berkeley Nicolas Verschueren Van Rees, Alan Champneys Dept of Physics University of Bristol [email protected] [email protected], [email protected]

MS19 MS18 A Geometric Approach to Stationary Defect Solu- Slow Dynamics of Localized Spot Patterns for tions Reaction-Diffusion Systems on the Sphere In this talk we consider the impact of a very simple and In the singularly perturbed limit corresponding to large small spatial heterogeneity on the existence of localized a diffusivity ratio between two components in a reaction- patterns in a system of PDEs in one spatial dimension. diffusion (RD) system, many such systems admit quasi- The existence problem reduces to the problem of finding a equilibrium spot patterns, where the solution concentrates heteroclinic orbit in an ODE in ‘time’ x, for which the vec- at a discrete set of points in the domain. In this context, we tor field for x ¿ 0 differs slightly from that for x ¡ 0, under derive and study the differential algebraic equation (DAE) the assumption that there is such an orbit in the unper- that characterizes the slow dynamics for such spot patterns turbed problem. We show that both the dimension of the for the Brusselator model on the surface of a sphere. Local- problem as well as the nature of the linearized system near ized spot patterns can undergo a fast time instability and the endpoints of the heteroclinic orbit has a remarkably we derive the conditions for this phenomena, which depend rich impact on the existence these defect solutions. on the spatial configuration of the spots and the parame- Arjen Doelman ters in the system. In the absence of these instabilities, Mathematisch Instituut our numerical solutions of the DAE system for N =2to [email protected] N = 8 spots suggest a large basin of attraction to a small set of possible steady-state configurations. We discuss the connections between our results and the study of point vor- Peter van Heijster tices on the sphere, as well as the problem of determining Mathematical Sciences School a set of elliptic Fekete points, which correspond to globally Queensland University of Technology minimizing the discrete logarithmic energy for N points on [email protected] the sphere. Feng Xie Philippe H. Trinh Mathematisch Instituut, Leiden University Program in Applied and Computational Mathematics Dept. of Appl. Math., Donghua University Princeton University [email protected] [email protected] MS19 Michael Ward Department of Mathematics Reformulating Spectral Problems with the Krein University of British Columbia Matrix [email protected] Successful resolution of spectral problems in Hamiltonian systems require that we locate not only the eigenvalues, MS18 but we also determine the Krein signature of those which are purely imaginary. The well-known Evans function de- The Origin of Finite Pulse Trains: Homoclinic termines the location and multiplicity of the eigenvalues, Snaking in Excitable Media but in its classical form it does not allow a determination of the signature. On the other hand, the Krein matrix, Many physical, chemical and biological systems exhibit and the accompanying Krein eigenvalues, allow us to not traveling waves as a result of either an oscillatory insta- only find the eigenvalues, but the graphs can be used to bility or excitability. The latter may admit a large mul- determine the signature. We will briefly consider the con- tiplicity of stable and spatially localized wavetrains con- struction of the matrix, and discuss its role in applications. sisting of different numbers of traveling pulses. The ex- istence of these states is related here to the presence of homoclinic snaking in the vicinity of a subcritical, finite Todd Kapitula wavenumber Hopf bifurcation. The pulses are organized Calvin College in a slanted snaking structure resulting from the presence Dept of Math & Statistics of a heteroclinic cycle between small and large amplitude [email protected] traveling waves. Connections of this type require a multi- valued dispersion relation. This dispersion relation is com- puted numerically and used to interpret the profile of the MS19 pulse group. The different spatially localized pulse trains Stability in Spatially Localized Patterns can be accessed by appropriately customised initial stimuli thereby blurring the traditional distinction between oscil- Motivated by numerical stability results on spatially local- latory and excitable systems. ized patterns in spatially extended systems, we show how the stability of patterns that are formed of nonlocalized Arik Yochelis fronts can be understood from the spectra of the underly- Jacob Blaustein Institutes for Desert Research, Sede ing fronts. We use extended Evans functions to understand Boqer the spectral properties of these patterns on the original un- Ben-Gurion University of the Negev bounded domain and on large but bounded domains and [email protected] compare our results to previous findings on resonance poles DS15 Abstracts 131

and edge bifurcations. in a wide range of systems, including Turing instability in activator-inhibitor systems and the dynamics of generators Elizabeth J. Makrides in power grids. Brown University Division of Applied Mathematics Takashi Nishikawa, Adilson E. Motter elizabeth [email protected] Northwestern University [email protected], [email protected] Bjorn Sandstede Division of Applied Mathematics Brown University MS20 bjorn [email protected] Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks MS19 Many networks are observed to produce patterns of syn- Existence of Pearled Patterns in the Planar Func- chronized clusters, but their prediction in general is dif- tionalized Cahn-Hilliard Equation ficult. We use computational group theory to find net- work symmetry and cluster synchronization. The number The functionalized Cahn-Hilliard (FCH) equation supports of symmetries can be astronomically large. We show this planar and circular bilayer interfaces as equilibria which experimentally using an electro-optic network. We observe may lose their stability through the pearling bifurcation: a a surprising phenomenon (isolated desynchronization) in periodic, high-frequency, in-plane modulation of the bilayer which some clusters lose synchrony while leaving others thickness. In two spatial dimensions we employ spatial dy- connected to them synchronized. This is explained by a namics, a center manifold reduction, normal form analy- subgroup decomposition of the group. sis and a fixed-point-theorem argument to show that the reduced system admits a degenerate 1:1 resonant normal Louis M. Pecora form, from which we deduce that the onset of the pearling Naval Research Lab bifurcation coincides with the creation of a two-parameter [email protected] family of pearled equilibria which are periodic in the in- plane direction and exponentially localized in the trans- verse direction. Francesco Sorrentino University of New Mexico Qiliang Wu Department of Mechanical Engineering Michigan State University [email protected] [email protected] Aaron M. Hagerstrom University of Maryland MS20 [email protected] HomeostasisAsaNetworkInvariant Rajarshi Roy The simplest mathematical definition of homeostasis is as University of Maryland, College Park, MD, USA follows. Suppose a system X˙ = F (X) has a stable equilib- [email protected] rium X0 and the system depends on an input parameter 0 I. Homeostasis occurs when one of the variables of X (I) Thomas E. Murphy th —saythej — is approximately constant over a broad University of Maryland, College Park range of I. We translate finding homeostasis to finding sin- Dept. of Electrical and Computer Engineering ∂X0 j [email protected] gular points ∂I (I0) = 0. We discuss the question: When are homeostasis singularities invariants of the system when viewed as a network? MS20 Martin Golubitsky Symmetry Breaking and Synchronization Patterns Ohio State University in Networks of Coupled Oscillators Mathematical Biosciences Institute [email protected] In a recent paper [1] we considered the dynamics of a col- lection of oscillators coupled to form a network and we Ian Stewart showed that the analysis of the network symmetries can University of Warwick be used to predict the emergence of cluster synchroniza- [email protected] tion patterns. In particular, we focused on a specific solu- tion corresponding to the partition of the network nodes in clusters, characterized by the ‘maximal symmetry’. In gen- MS20 eral, given a network, there are other cluster synchronous Optimized Networks Have Cusp-like Dependence solutions that may emerge, which correspond to symmetry on Structural Parameters breakings of the maximal symmetry solution. While in [1], we presented a method to characterize this one solution Using synchronization stability as a prototypical exam- and its stability, we will try to extend this approach to the ple, we demonstrate a general phenomenon observed in ‘lower symmetry’ solutions. In particular, we will outline a complex networks of coupled dynamical units: the opti- procedure to exhaustively study the existence and stabil- mization of collective dynamics leads to cusp-like depen- ity of all these solutions. [1] L. M. Pecora, F. Sorrentino, dence on network-structural parameters, such as the num- A. M. Hagerstrom, T. E. Murphy, R. Roy, ”Cluster Syn- ber of nodes/links and the magnitude of structural per- chronization and Isolated Desynchronization in Complex turbations. We show that this phenomenon is observed Networks with Symmetries”, Nature Communications, 5, 132 DS15 Abstracts

4079 (2014) at MIT.

Francesco Sorrentino Pierre Lermusiaux University of New Mexico MIT Department of Mechanical Engineering [email protected] [email protected] MS21 Aaron M. Hagerstrom University of Maryland Optimal Control in Lagrangian Data Assimilation [email protected] Inferring the state of an ocean flow is an integral part of environmental monitoring. Autonomous vehicles with a Louis M. Pecora limited capacity for locomotion are increasingly being used Naval Research Lab for data assimilation of various quantities of interest in the [email protected] ocean, including the underlying time-independent velocity field. We assess the efficacy of optimal control techniques Thomas E. Murphy to guide Lagrangian data assimilation in 2-dimensional University of Maryland, College Park flows, focusing on assimilation of the velocity field itself. Dept. of Electrical and Computer Engineering [email protected] Damon Mcdougall Institute for Computational Engineering Sciences Rajarshi Roy The University of Texas at Austin University of Maryland, College Park, MD, USA [email protected] [email protected] Richard O. Moore New Jersey Institute of Technology MS21 [email protected] A Multi Agent Control Strategy for Sampling Un- certain Spatio-Temporally Varying Flow Fields MS21 A Hybrid Particle-Ensemble Kalman Filter for Uncertainties are a key factor when measuring geophys- High Dimensional Lagrangian Data Assimilation ical flows to determine optimal positions for mobile sen- sors. To include uncertainties with a physical model of the We apply the recently proposed hybrid particle-ensemble environment, a model-based observer framework is used, Kalman filter to assimilate Lagrangian data into a non- which integrates measurements from sensors and propa- linear, high dimensional quasi-geostrophic ocean model. gates the estimated field by computational fluid dynamics. Effectively the hybrid filter applies a particle filter to the Spatiotemporal flow, concentration and uncertainty layers highly nonlinear, low-dimensional Lagrangian instrument of this observer are combined with importance and colli- variables while applying an ensemble Kalman type update sion avoidance maps to generate optimal paths for a team to the high-dimensional Eulerian flow field. We will present of underactuated autonomous sampling vehicles. some initial results and discuss both challenges and oppor- tunities that this strategy provides. Axel Hackbarth Hamburg University of Technology Elaine Spiller [email protected] Marquette University [email protected] Edwin Kreuzer Institute of Mechanics and Ocean Engineering Laura Slivinski Hamburg University of Technology Woods Hole Oceanographic Institution [email protected] [email protected]

Amit Apte MS21 TIFR Centre for Applicable Mathematics Bangalore, India Bayesian Nonlinear Assimilation for Eulerian [email protected] Fields and Lagrangian Trajectories

We consider the Bayesian nonlinear assimilation of Eule- MS22 rian and Lagrangian flow data, exploiting nonlinear gov- The Geometry of the Toda Lattice Map erning equations and mutual information structures inher- ent to coastal ocean dynamical systems and optimally in- In this talk we consider some of the geometry behind the ferring the corresponding multiscale fields and transports. Flaschka coordinates for the Toda lattice equations. We Our Bayesian nonlinear smoothing combines reduced-order show in particular that the Flaschka mapping is a momen- Dynamically-Orthogonal equations with Gaussian Mixture tum map and indicate how it can be generalized to study Models, extending linearized backward pass updates to a related systems such as rigid body flows on lower triangu- Bayesian nonlinear setting. This mutual information trans- lar matrices. This is joint work with Francois Gay-Balmaz fer, both forward and backward in time, is linked to La- and Tudor Ratiu. grangian concepts, coherent structures and optimal sam- pling. Examples are provided with a focus on transports in Anthony M. Bloch fluid flows. This is joint work with Tapovan Lolla, Patrick University of Michigan Haley, Jing Lin, Deepak Subramani and our MSEAS group Department of Mathematics DS15 Abstracts 133

[email protected] strained dynamics.

Dmitry Zenkov MS22 North Carolina State University Department of Mathematics Geodesic Finite Elements on Symmetric Spaces [email protected] and Their Applications to Multisymplectic Varia- tional Integrators MS23 To obtain multisymplectic discretizations of Hamiltonian PDEs with symmetries, we introduce group-equivariant Self-Oscillations Via Two-Relay Controller: De- geodesic finite-element spaces that take values in symmet- sign, Analysis, and Applications ric spaces. This is achieved by endowing symmetric spaces, Limit cycles induced by relay feedback systems and its ap- and in particular, the space of positive-definite matrices, plication to underactuated mechanical systems will be ad- Lorentzian matrices, and symplectic matrices, with a Rie- dressed. Particularly, a two-relay controller (TRC) is pro- mannian metric structure that is induced by a metric on posed for generation of Self-Oscillations (SO) in dynamic the general linear group. This allows us to apply the Rie- systems. The design procedures are proposed using three mannian center of mass construction to obtain manifold- methodologies: the one based on DF, on Poincar´emaps, valued shape functions. and on Locus of Perturbed Relay System method. The results are illustrated by experiments on SO generation in Phillip Grohs a wheel pendulum, Furuta pendulum, and a 3-DOF heli- ETH Zurich copter. Seminar for Applied Mathematics [email protected] Luis T. Aguilar CITEDI-IPM Melvin Leok [email protected] University of California, San Diego Department of Mathematics Igor Boiko [email protected] The Petroleum Institute [email protected] Joe Salamon University of California, San Diego Leonid Fridman, Rafael Iriarte Department of Physics Universidad Nacional Autonoma de Mexico [email protected] [email protected], [email protected]

John Moody University of California, San Diego MS23 Department of Mathematics Periodic Solutions in Dynamical Systems with Re- [email protected] lay: Existence, Stability, Bifurcations

We consider a system of ordinary differential equations MS22 with hysteresis of a relay type. In particular, such a sys- Dynamics and Optimal Control of Flexible Solar tem describes diffusion equations with hysteretic control on Updraft Towers the boundary. We analyze existence, stability, and bifur- cations of periodic solutions. Furthermore, we show that The use of solar chimneys for energy production has been additional time-delay terms can favorably change the sta- suggested more than 100 years ago but was hampered in bility of periodic solutions. The first part of our talk is large part due to the high cost of erecting tall towers. Re- based on a joint work with Sergey Tikhomirov and the cently, alternative technique of flexible towers built of in- second part with Eyal Ron. flatable toroidal bladders was suggested. We develop a ge- ometric theory of motion and control of such towers, and Pavel Gurevich Free University Berlin report on the results of experiments demonstrating the re- [email protected] markable stability of the tower in real-life conditions.

Vakhtang Putkaradze MS23 University of Alberta [email protected] Population Dynamics with the Preisach Operator We consider population dynamics models where species (individuals) can switch between two modes of behavior MS22 in response to exogenous stimuli. The switching rule of Hamel’s Formalism for Infinite-Dimensional Me- each individual is modeled by a two-threshold non-ideal chanical Systems relay; the averaged state of the individuals feeds back into the system. We consider the SIR and predator-prey type Hamel’s formalism is a form of Lagrangian mechanics that models extended by these switching dynamics and discuss generalizes both Euler-Lagrange and Euler-Poincare equa- continuous sets of equilibria, robust homoclinic trajectories tions. This is accomplished by unlinking the configuration and other dynamics. and velocity measurements. The use of this formalism of- ten leads to a simpler representation of dynamics. This talk Dmitry Rachinskiy will introduce Hamel’s formalism for infinite-dimensional Department of Mathematical Sciences mechanical systems and demonstrate its utility in con- University of Texas at Dallas 134 DS15 Abstracts

[email protected] invariant sets afterwards.

Adam M. Fox MS23 Department of Mathematics Reaction-Diffusion Equations with Discontinuous Western New England University Relay Nonlinearity [email protected]

We consider reaction-diffusion equations involving a relay James D. Meiss discontinuity in the source term, which is defined at each University of Colorado spatial point. In particular, such problems describe chem- Dept of Applied Mathematics ical reactions and biological processes in which diffusive [email protected] and nondiffusive substances interact according to hystere- sis law. We show that behaviour of such systems essentially depends on the initial data. For the so-called transverse MS24 initial data we show that solutions of the problem can be Nontwist Worm Map described by a certain free boundary problem. In the case of non-transverse initial data values of the relay form a In this work we propose a nontwist discrete map to inves- spatially periodic or spatially quasyperiodic pattern that tigate how the confinement of chaotic regions affects the originates at a point and propagates outwards. topology of phase space. We choose to modify the Hamil- tonian that generates the standard nontwist map, in order Sergey Tikhomirov to create two linear barriers on the y-axis. As the perturba- Max Planck Institute for Mathematics in the Science tion is increased, we observe an onset of avoided regions not Chebyshev Laboratory, Saint-Petersburg State University visited by chaotic orbits initiated inside the range formed [email protected] by the introduced barriers. On the other hand, unstable manifolds from two hyperbolic fixed points, located out- Pavel Gurevich side the chosen region, can pass through these barriers, Free University Berlin filling the avoided regions generated by the confinement [email protected] proposed. The effect that allows the diffusion of chaotic orbits in only certain directions is known as the ratchet ef- fect, which has been extensively studied in dissipative and MS24 Hamiltonian systems, due to its relevance in biology and Influence of Finite Larmor Radius on Critical Pa- nanotechnology. The possible observation of the ratchet rameters for Invariant Curves Break Up in Area effect in our map motivates our analyses. Preserving Maps Models of ExB Chaotic Transport CarolineG.L.Martins We consider 2-dimensional area preserving maps describ- Institute for Fusion Studies ing chaotic transport in magnetized plasmas with zonal [email protected] flows perturbed by electrostatic drift waves. We include finite Larmor radius effects by gyro-averaging the corre- P. J. Morrison sponding Hamiltonians of the nontwist maps. Dynamical Department of Physics and Institute of Fusion Studies systems methods based on recurrence time statistics are The University of Texas at Austin used to quantify the dependence on the Larmor radius of [email protected] the threshold for the destruction of shearless transport bar- riers. J. D. Szezech Universidade Estadual de Ponta Grossa Julio Fonseca [email protected] University of Sao Paulo [email protected] I. L. Caldas Universidade de So Paulo Diego Del-Castillo-Negrete Instituto de Fsica Oak Ridge National Laboratory [email protected] [email protected]

Iber L. Caldas MS24 Instituto de Fsica, Universidade de So Paulo Breakup of Shearless Tori and Reconnection in the [email protected] Piecewise-Linear Standard Nontwist Map

A piecewise-linear version of the area-preserving stan- MS24 dard nontwist map is considered as a simple model of a Breakup of Tori in Multiharmonic Nontwist Stan- piecewise-smooth map which also violates the twist con- dard Maps dition. Using symmetry lines and involutions, I compute periodic orbits to analyze periodic orbit collisions and sep- Invariant circles play a prominent role in the dynamics of aratrix reconnection. The transition to chaos due to the area-preserving maps. Unfortunately, much of the theory destruction of the shearless curve with rotation number developed to study these circles in twist maps does not equal to the inverse golden mean is studied using Greene s apply to nontwist systems. In this talk we will employ a residue criterion. quasi-Newton, Fourier-based method to compute the con- jugacies of the circles. We will then demonstrate how the Alexander Wurm near-critical conjugacies provide insight into the mechan- Department of Physical & Biological Sciences ics of the breakup of the circles and the topology of the Western New England University DS15 Abstracts 135

[email protected] circuit underlying swimmeret coordination provides a ro- bust mechanism for generating this stroke pattern.

MS25 Tim Lewis The Role of Voltage-Dependent Electrical Coupling University of California, Davis in the Control of Oscillations [email protected]

We focus on the role of voltage-dependent electrical cou- pling in determining existence, stability and qualitative MS25 properties of solutions in the crab gastric mill rhythm. Understanding and Distinguishing Multiple Time The network consists of a mutually inhibitory pair of neu- Scale Oscillations rons that receive electrical input from a particular projec- tion neuron together with the synaptic input from a pace- CPGs may exhibit behavior, including bursting, involving maker neuron. Using singular perturbation techniques and multiple distinct time scales. Our goal is to understand phase-plane space analysis, we derive and analyze a low- bursting dynamics in multiple-time-scale systems, moti- dimensional map that encodes the effects of these distinct vated by a model of respiratory CPG neuron. We ap- inputs. ply geometric singular perturbation theory to explain the mechanisms underlying some interesting forms of bursting Christina Mouser dynamics involving multiple forms of activity within each William Patterson University cycle. We consider how many time scales are involved, [email protected] obtaining some non-intuitive results, and identify solution properties that truly require three time scales. Farzan Nadim New Jersey Institute of Technology Yangyang Wang &RutgersUniversity University of Pittsburgh [email protected] [email protected]

Amitabha Bose Jonathan E. Rubin New Jersey Inst of Technology University of Pittsburgh Department of Mathematical Sciences Department of Mathematics [email protected] [email protected]

MS25 MS26 The Essential Role of Phase Delayed Inhibition in Decoding Synchronized Oscillations How Small a Thought: Design of Mixing and Sep- aration Processes with Dynamical Systems The widespread presence of synchronized neuronal oscilla- tions in the brain suggests the existence of a mechanism We use dynamical systems to design manufacturing pro- that can decode such activity. Candidate mechanisms in- cesses. Two examples are: (1) The Rotated Arc Mixer, clude: high-spike threshold detection (HTD) and phase- an embodiment of the KAM theorem, increases manufac- delayed inhibition (PDI). Despite being more complex, PDI turing productivity 25% and decreases mixing energy 95%. has been observed in multiple systems, suggesting an in- (2) The dynamical system for inertial particles in a laminar herent advantage over the alternative. We show that PDI flow has both attracting and repelling regions, the interplay is capable of detecting synchrony far more robustly than of which localizes particles when the Reynolds number ex- HTD, making the motif essential in any system with noisy ceeds a critical value with applications in solid-liquid sep- encoders. arations. The predicted instability boundary agrees well with data. Badal Joshi California State University, San Marcos Guy Metcalfe [email protected] CSIRO Materials Science & Engineering Melbourne, Australia Mainak Patel [email protected] College of William and Mary [email protected] MS26 3D Chaotic Advection in Langmuir Cells MS25 Neural Mechanisms of Limb Coordination in Crus- We investigate Lagrangian transport processes in a row of tacean Swimming horizontally aligned, vertically sheared, alternating cylin- drical vortices: a simple model of ocean Langmuir circula- Long-tailed crustaceans swim by rhythmically moving tions. We map out the chaotic regions and barriers that re- limbs called swimmerets. Over the entire biological range sult when the system is subject to three-dimensional steady of animal size and paddling frequency, movements of adja- and unsteady disturbances. Chaotic advection occurs in cent swimmerets maintain an approximate quarter-period resonant layers within each Langmuir cell, and exchange phase difference with the more posterior limbs leading the between the cells via three-dimensional turnstile lobes also cycle. Recently we have demonstrated that this frequency- occurs. invariant stroke pattern is the most effective and mechan- ically efficient paddling rhythm across the full range of bi- Larry Pratt ologically relevant Reynolds numbers in crustacean swim- Woods Hole Oceanographic Inst. ming. Here, we argue that the organization of the neural [email protected] 136 DS15 Abstracts

Irina Rypina Imperial College London Woods Hole Oceanographic Institution Rice University [email protected] michael.j.fi[email protected]

Anushaya Mohapatra MS26 Oregon State University Chaotic Mixing and Transport Barriers [email protected] We present experiments on chaotic transport in two- and three-dimensional flows. The 2D flows are oscillating vor- MS27 tex chains with a wind that produces L´evy flights and su- Pulse Bifurcations in Stochastic Neural Fields perdiffusive transport. We consider two 3D flows: (a) a nested vortex chain flow, which gives rise to chaotic mix- We study the effects of additive noise on traveling waves ing even if the flow is time-independent; and (b) a vortex in spatially extended neural fields. Neural fields equations chain with Ekman pumping for which all transport barriers have an integral term, characterizing synaptic interactions can be destroyed even for arbitrarily small time-dependent between neurons at different spatial locations of the net- perturbations. work. Traveling pulse solutions emerge when considering the effects of local negative feedback, generating a drift Thomas H. Solomon instability. Near this criticality, we derive a stochastic am- Department of Physics & Astronomy plitude equation describing the pulse dynamics when the Bucknell University noise and the deterministic instability are of comparable [email protected] magnitude.

MS26 Zachary Kilpatrick University of Houston Experimental Investigation of Fundamental La- [email protected] grangian Transport Phenomena

Principal goal is experimental validation of the predicted Gregory Faye ´ response of a prototypical 3D unsteady flow with spheroidal Ecole des hautes ´etudes en sciences sociales (as opposed to toroidal) invariant surfaces to weak pertur- [email protected] bations. Investigated are fundamental features as symme- tries and periodic lines in the unperturbed state and the formation of tubular structures upon weak perturbation. MS27 The latter promote global transport and, ultimately, 3D Classifying Bifurcations in Coupled Cell Networks chaos. Moreover, the experiments validate the essential in- dependence of this response upon the particular nature of Stewart and Golubitsky observed that robust synchrony the perturbation. in coupled cell networks is determined by quotient net- works. This result was recently generalized by DeVille and Michel Speetjens Lerman, who noted that any so-called ‘graph fibration’ in- Laboratory for Energy Technology, Dept. Mech. Eng. duces a conjugacy between the dynamics of a network and Eindhoven University of Technology its quotients. Starting from the simple observation that [email protected] any ‘self-fibration’ hence induces a symmetry, we present a theory of center manifold reduction that is specifically suited for coupled cell networks. MS27 Dynamics of Asynchronous Networks Eddie Nijholt, Bob Rink, Jan Sanders VU University Amsterdam Systems that have the structure of a network of intercon- [email protected], [email protected], nected nodes are abundant in nature and technology. Many [email protected] mathematical models of such networks are given as ordi- nary differential equations defined by smooth vector fields. These traditional or “synchronous’ network models, how- MS27 ever, fail to incorporate features seen in real world; for Dynamics of Heterogeneous Networks: Reductions example, individual components of a network cannot stop and Coherent Behaviour and restart in finite time. Asynchronous networks are an attempt to set up a mathematical framework to study sys- Recent experiments show that networks exhibit multiple tems that exhibit stopping of nodes and their bifurcations. levels of coherent dynamics depending on the connectivity We compare our framework to traditional approaches of level of the network. Striking examples are found in the differential equations with discontinuous vector fields and brain. Indeed, synchronisation between highly connected show equivalence under certain assumptions. We also ex- neurons coordinate and shape development in hippocampal plore deadlocks as specific dynamical states in which all networks. We provide a probabilistic approach for random nodes stop and never restart. These states cannot occur networks with chaotic dynamics. We develop a reduction in a synchronous setup but are a natural feature of asyn- technique to describe the dynamics of the highly connected chronous settings. network layers in terms of the network’s microscopic de- tails. Christian Bick Max Planck Institute for Dynamics and Self-Organization: Tiago Pereira [email protected] Department of Mathematics Imperial College, London, UK Michael Field [email protected] DS15 Abstracts 137

Matteo Tanzi, Sebastian van Strien Aaron M. Hagerstrom, Joseph Hart Imperial College London University of Maryland [email protected], [email protected] [email protected], [email protected]

Thomas E. Murphy MS28 University of Maryland, College Park Oscillatory Dynamics of the Candelator Dept. of Electrical and Computer Engineering [email protected] We describe the dynamics of the popular “candle see-saw” experiment in which a candle lit at both ends undergoes Rajarshi Roy vertical oscillations as liquid wax drips from either end. We ◦ University of Maryland compare existing theory for small oscillations (θ<30 )and [email protected] numerical simulations for large oscillations to experimental data.

Greg A. Byrne, Mary Elizabeth Lee, Flavio Fenton MS28 Georgia Institute of Technology [email protected], [email protected], Noise-Induced Transitions in Bistable Tunnel fl[email protected] Diode Circuits

We measure first-passage time distributions of electrical MS28 current switching in a bistable tunnel diode circuit driven Period Doubling in the Saline Oscillator with adjustable noise intensity. Near a saddle-node bifur- cation, the logarithm of mean switching time scales linearly We provide today a simple, nonlinear system that captures with distance to the bifurcation point and inversely with many aspects of cardiac dynamics. The saline oscillator is noise intensity. This suggests a noise-induced switching a two chambered plastic box with one orifice connecting the process that is mediated by nucleation to a distinct state two chambers. There is a jet of fluid flowing through the of current flow, with nucleation occurring either at the edge orifice. Along with this jet is a local voltage that parallels or interior of the diode. the flow of the jet. The voltage from the saline oscilla- tor highly resembles an action potential and can produce period one and period two cycles. Stephen Teitsworth, Yuriy Bomze, Steven Jones, Ryan McGeehan Diandian Diana Chen Duke University Georgia Institute of Technology [email protected], [email protected], sci- School of Physics [email protected], [email protected] [email protected]

Flavio Fenton MS29 Georgia Institute of Technology fl[email protected] Population Models Applied to Model the Preg- nancy to Labor Transition

MS28 In human pregnancy the steroid hormone progesterone acts Synchronization Patterns in Simple Networks of via two receptors designated PR-A and PR-B. At term Optoelectronic Oscillators PR-A interferes with PR-B’s anti-inflammatory function to initiate labor. We present a model of PR-B’s interac- Simple motifs are important constituents of complex net- tions with inflammation and use the dimensionless model works; insight into the patterns of synchrony for differ- to predict the onset of labor in two human transcriptome ent connection topologies is relevant to understanding how datasets. Solving the dimensionless model allows us to plot they perform different dynamical functions. Global syn- the trajectory of a womans pregnancy in time and study chrony, the formation of clusters and desynchronized be- the dynamics of the PR-A/PR-B interaction. havior are all aspects of operation that are observed in the experiments we describe on coupled optoelectronic oscilla- tors. We explore the dependence of these patterns of syn- Douglas Brubaker chrony and their stability in relationship to the symmetries CWRU School of Medicine of the network motifs. Center for Proteomics and Bioinformatics [email protected] Briana Mork University of Maryland Alethea Barbaro [email protected] Case Western Reserve University [email protected] Kate Coppess University of Michigan Mark Chance Ann Arbor, MI USA Case Western Reserve University [email protected] Center for Proteomics and Bioinformatics [email protected] Caitlin R. S. Williams University of Maryland Sam Mesiano Dept. of Physics Case Western Reserve University Dept. of Reproductive [email protected] Biolog 138 DS15 Abstracts

[email protected] crowd.

Jesus Rosado Linares MS29 Universidad de Buenos Aires - CONICET Stochastic Fluctuations in Suspensions of Swim- Departamento de Matematica ming Microorganisms [email protected]

Mean field theories have had a good deal of success in ex- Alethea Barbaro plaining many features regarding the remarkable dynamics Case Western Reserve University of suspensions of swimming microorganisms, including the [email protected] onset of patterned motion in certain parameter regimes. We describe an extension of these mean field theories to Andrea L. Bertozzi include stochastic fluctuations in the density of the swim- UCLA Department of Mathematics ming microorganisms, and some computational issues in [email protected] simulating the resulting stochastic partial differential equa- tions.

Peter R. Kramer MS30 Rensselaer Polytechnic Institute A Self-Organising Distributed Strategy for Optimal Department of Mathematical Sciences Synchronisation of Networked Mechanical Systems [email protected] We consider the problem of adapting a weighted graph in a Yuzhou Qian distributed fashion to maximise a desired cost function, as Rensselaer Polytechnic Institute for instance the algebraic connectivity of the graph subject [email protected] to constraints such as maximum weighted degree at each node and non-negativity of edge weights. The proposed Patrick Underhill method adapts edge weights in continuous time and is ro- Rensselaer Polytechnic Institute bust to topological changes in the network. We apply the Department of Chemical and Biological Engineering strategy to solve the problem of optimising synchronisation [email protected] in a network of coupled mechanical systems.

MS29 Louis Kempton, Guido Hermann University of Bristol, UK A Model for Riot Dynamics: Shocks, Diffusion and [email protected], [email protected] Thresholds

In this talk I will introduce variants of a system of differ- Mario Di Bernardo ential equations that model social outbursts, such as riots. University of Bristol The systems involves coupling of an explicit variable repre- Dept of Engineering Mathematic senting the intensity of rioting activity and an underlying [email protected] (implicit) field of social tension. Our models include the ef- fects of exogenous and endogenous factors as well as various propagation mechanisms. I will discuss various properties MS30 of this system, including the existence of traveling wave Synchronization in Dynamical Networks of Noisy solutions whose speed experiences a transition based on a Nonlinear Oscillators, Or Collective Behavior of critical threshold for the social tension. Zebrafish Nancy Rodriguez-Bunn University of North Carolina at Chapel Hill Zebrafish is a popular laboratory animal species for the Department of Mathematics investigation of several functional and dysfunctional bio- [email protected] logical processes. Their burst-and-coast swimming style is well described through a stochastic mean reverting jump Henri Berestycki, Jean-Pierre Nadal diffusion model. Here, we analyze zebrafish schooling by CMAS-EHESS modeling their social interactions through a noisy vectorial [email protected], [email protected] network model, in which each fish is assimilated to a net- work node whose neighbors are randomly and uniformly se- lected from the group. Through numerical simulations and MS29 closed-form results, we assess the role of the network size, number of neighbors, and noise features on the stochastic Crowd Modeling: How Can People Respond to synchronization. Fear

We present a model for crowd dynamics where the motion Violet Mwaffo, Ross Anderson of individuals is assumed to depend on their level of ex- Dept. of Mechanical and Aerospace Engineering citement (or fear) and thus the mechanism by which the New York University Polytechnic School of Engineering emotion spreads play an important role. We start with an vmwaff[email protected], [email protected] agent based Cucker-Smale-like model for which we derive the continuity equation from the mean field limit and an- Maurizio Porfiri alyze their asymptotic behavior. Then we explore numeri- Dept. of Mechanical, Aerospace and Manufacturing cally how variations, in both the effects of the emotion and Engineering its mechanism of propagation, affects the dynamics of the Polytechnic University DS15 Abstracts 139

mporfi[email protected] the mechanisms behind these transitions as well as the im- pact of the coupling topology on the observed phenomena.

MS30 Gerrit Ansmann, Klaus Lehnertz Synchronization of a Nonlinear Beam Coupled with Department of Epileptology Deformable Substrates University of Bonn, Germany [email protected], [email protected] The nonlinear dynamics of a distributed mechanical sys- tem comprised of a beam mechanically coupled with a de- Ulrike Feudel formable substrate is considered. A mathematical model University of Oldenburg of the coupled system is constructed with the inclusion ICBM, Theoretical Physics/Complex Systems of beam’s geometric nonlinearities and the combined ef- [email protected] fect of strain and strain rate in the material response of the substrate. Synchronization between the beam and the substrate is formally investigated through the evolution of MS31 the governing system on nonlinear partial differential equa- tions. It is shown how locomotion of the beam can be Extreme Events in Nature: Harmful Algal Blooms achieved by synchronization with motions of the substrate, and how material and geometric properties of the substrate Harmful algal blooms (HABs) are rare events in the ocean canbeinferredbysynchronizationwithimposedmotions characterized by a sudden large abundance of toxic phy- of the beam. tolankton species. We study the mechanism behind the emergence of HABs by modeling the population dynamics Davide Spinello as an excitable system involving the competition between University of Ottawa different activators, toxic and non-toxic species, as well the [email protected] preference of the inhibitor, the grazing zooplankton, for certain activators. We show how toxin production, hydro- dynamics and variable nutrient input influence the trigger MS30 mechanism. Synchronization Control of Electrochemical Oscil- lator Assemblies by External Inputs Ulrike Feudel University of Oldenburg We consider the manipulation of a collection of heteroge- ICBM, Theoretical Physics/Complex Systems neous nonlinear oscillators, which have unobservable state [email protected] and receive a common input, to form dynamical synchro- nization structures. Examining the conditions for entrain- Subhendu Chakraborty ment of an oscillator to a periodic input yields insight into DTU Aqua, Denmark a non-traditional control methodology. Phase coordinate [email protected] transformation, ergodic averaging, and novel waveform de- sign algorithms are used to produce inputs that establish Cornelius Steinbrink structures in the systems’ oscillation phases. The complex- University Oldenburg, Germany ity of realizable designs is limited by the nonlinearity and [email protected] heterogeneity of oscillators in the ensemble. The technique is applied successfully in experiments involving assemblies of electrochemical oscillators. Rajat Karnatak Theoretical Physics/Complex Systems, ICBM Anatoly Zlotnik University Oldenburg Washington University in St. Louis [email protected] [email protected] Helmut Hillebrand Istvan Z. Kiss University Oldenburg, Germany Department of Chemistry ICBM, Planktology Saint Louis University [email protected] [email protected]

Raphael Nagao MS31 Saint Louis University Forecasting and Controlling Dragon-King Events in [email protected] Coupled Dynamical Systems

Jr-Shin Li It is often believed that extreme events in dynamical sys- Washington University in St. Louis tem follow a scale-free, power-law probability distribution [email protected] and hence these events are unpredictable. We study ex- treme events in coupled chaotic oscillators and find that the largest events deviate from the power law distribution MS31 (so-called dragon-kings). We show that it is possible to Extreme Events on Small-World Networks of Ex- forecast in real time an impending dragon-king and that citable Units they can be suppressed by applying tiny perturbations to the system. We investigate small-world networks of excitable units that exhibit different types of collective dynamics, which include Daniel J. Gauthier extreme events. The transitions between the different types Duke University of dynamics are irregular and self-generated. We discuss [email protected] 140 DS15 Abstracts

Hugo Cavalcante for Energy Absorption and Harvesting Departamento de Informatica Universidade Federal da Paraiba The nonlinear dynamics of a two-degree-of-freedom system [email protected] consisting of a linear oscillator (LO) coupled to a bistable light attachment (NES) is investigated. The parameters of Marcos Oria the bistable NES are optimized in order to make it func- Grupo de Fisica Atomica e Lasers-DF tioning as a linear TMD for low-amplitude, in-well, oscil- Universidade Federal da Paraiba lations. The energy transfer mechanisms between the LO [email protected] and the NES are discussed in order to assess the potential of this configuration for absorption and harvesting purposes. Didier Sornette Department of Management, Technology and Economics Francesco Romeo ETH Zurich University of Rome - La Sapienza [email protected] [email protected]

Ed Ott Giuseppe Habib University of Maryland University of Liege [email protected] [email protected]

MS31 MS32 Extreme Events in Stochastic Multistable Systems Stochastic Closure Schemes for Bi-stable Energy Harvesters Excited by Colored Noise Pulses with extremely large amplitude appear in a system with coexisting attractors subject to stochastic processes. The goal of this work is the development of a closure We demonstrate the emergence of such pulses in fiber and methodology that can overcome the limitations of tra- semiconductor lasers close to saddle-node bifurcations, and ditional statistical linearization/Gaussian closure schemes show how their probability depends on noise and laser pa- and can approximate the steady state statistical structure rameters. of bistable systems. Our approach is based on the mini- mization of a cost functional that expresses i) second-order Alexander N. Pisarchik moment information for the dynamics and ii) pdf represen- Centro de Investigaciones en Optica tation constraints for bi-stable systems. Our results com- [email protected] pare favorably with direct Monte-Carlo simulations.

Ricardo Sevilla-Escoboza, Guillermo Huerta-Cuellar, Themistoklis Sapsis Rider Jaimes-Re´ategui Massachusetts Institute of Techonology Centro Universitario de los Lagos [email protected] Universidad de Guadalajara [email protected], [email protected], Han Kyul Joo [email protected] MIT [email protected] MS32 Convergent Heat Conduction in One-Dimensional MS32 Lattices with Dissociation Acceleration of Charged Particles in the Presence of Fluctuations The paper considers highly debated problem of conver- gence of heat conductivity in one-dimensional chains. We We consider resonances-driven acceleration and energy conjecture that the convergence may be promoted due to transport of charged particles in the earth magnetotail in possibility of the chain to dissociate. To clarify this point, the presence of high-frequency fluctuations of the back- we study the simplest model of this sort – a chain of linearly ground magnetic field. We show that fluctuations signifi- elastic rods with finite size. Formation of gaps between the cantly affect both capture into resonance, by forcing parti- rods is the only possible mechanism for scattering of the cles to escape from the surfatron resonance and thus alter- elastic waves. Heat conduction in this system turns out to ing the resulting energy spectrum of particles; and scatter- be convergent. Moreover, an asymptotic behavior of the ing by resonance, by changing the structure of beamlets, heat conduction coefficient for the case of large densities which are regular islands in chaotic sea. and relatively low temperatures obeys simple Arrhenius- type law. Africa Ruiz Mora, Dmitri Vainchtein Dept. of Mechanical Engineering Oleg Gendelman Temple University, USA Technion Israel Institute of Technology [email protected], [email protected] [email protected]

Alexander Savin MS33 Institute of Chemical Physics, Moscow, Russia Models of Large Deviations and Rare Events for [email protected] Optical Pulses

In optical systems, amplified spontaneous emission noise MS32 leads to errors if noise-induced fluctuations are large. We Bistable Nonlinear Energy Sink Coupled System discuss methods for modeling large deviations in such sys- DS15 Abstracts 141

tems. In particular, we show how the problem of find- dykman at pa.msu.edu. ing large deviations can be formulated as a constrained optimization problem that combines the pulse evolution equation and, in some cases, a detector model. The re- MS33 sults of the combined optimization are then used to guide Rare Event Extinction on Stochastic Networks importance-sampled Monte-Carlo simulations to compute error probabilities. We consider stochastic extinction of an epidemic on a net- work. We use a pair-based proxy model for nodes and William Kath links for a susceptible-infected-susceptible (SIS) epidemic Department of Applied Mathematics, Northwestern on a random network. Extending the theory of large de- University viations to random networks, we predict extinction times Department of Neurobiology, Northwestern University and find the most probable path to extinction. Predictions [email protected] are shown to agree well with Monte Carlo simulations of the network.

Leah Shaw MS33 College of William and Mary Influence of Periodic Modulation in Extreme Opti- [email protected] cal Pulses Brandon S. Lindley Naval Research Laboratory Semiconductor lasers with optical injection display a rich [email protected] variety of behaviours, including extreme pulses, which have been identified as rogue waves (RWs). We have shown that RWs can be completely suppressed via direct current mod- Ira B. Schwartz ulation, with appropriated modulation amplitude and fre- Naval Research Laboratory quency. Here we show that, when RWs are not suppressed, Nonlinear Dynamical Systems Section their probability depends on the modulation phase. There [email protected] are “safe’ windows where no RWs occur. The most extreme RWs occur at the window boundary. MS34 A Mathematical Model of Cancer Stem Cell Lin- Cristina Masoller eage Population Dynamics with Mutation Accumu- Universitat Polit`ecnica de Catalunya (UPC lation and Telomere Length Hierarchies Departament de Fsica i Enginyeria Nuclear (DFEN) [email protected] Cancer develops when cells acquire a sequence of muta- tions, which determines a hierarchy among the cells, based on how many more mutations they need to accumulate in MS33 order to become cancerous. Telomere loss and differenti- ation define another cell hierarchy, on top of which is the Rare Events in Stochastic Dynamical Systems with stem cell. This mutation-generation model combines the Delay: From Random Switching to Extinctions mutation-accumulation hierarchy with the differentiation hierarchy of the cells, allowing us to take a step further in We consider delayed multi-attractor noise-induced switch- examining cancer acquisition and growth. ing, and extinction in populations systems with delay near bifurcation points. For weak noise, the rates of inter- Georgi Kapitanov attractor switching and extinction are exponentially small. Department of Mathematics Finding these rates is formulated as a set of acausal vari- Purdue University ational problems, which in turn give the most probable [email protected] paths followed in switching or extinction. Explicit gen- eral theoretical results obtained show the analytical results agree well with the numerical simulations for both switch- MS34 ing and extinction rates. How Much and How Often? Mathematical Models of Cancer Vaccine Delivery Ira B. Schwartz Naval Research Laboratory Cancer immunotherapy was heralded as the Breakthrough Nonlinear Dynamical Systems Section of the Year 2013 by Science magazine due to innovations [email protected] in strategies to harness the immune system to fight can- cer. Yet many questions remain unanswered: What is the correct mixture of therapies to give, in what order should Thomas W. Carr they be given, and according to what schedule? In this Southern Methodist University talk I will present mathematical models that can be used Department of Mathematics to suggest answers to these questions. [email protected] Ami Radunskaya Lora Billings Pomona College Montclair State University Mathematics Department Dept. of Mathematical Sciences [email protected] [email protected]

Mark Dykman MS34 Michigan State University A Cell Population Model Structured by Cell Age 142 DS15 Abstracts

Incorporating Cell-cell Adhesion tal Diffusion

An analysis is given of a continuum model of a proliferating We study the advection dynamics of inertial particles in cell population, which incorporates cell movement in space order to understand the sedimentation of marine snow. In and cell progression through the cell cycle. The model this work we analyze the effect of the Basset force, an inte- consists of a nonlinear partial differential equation for the gral over the particle’s history, on the advection of slowly cell density in the spatial position and the cell age coordi- moving, dense or nearly neutral particles in the presence nates. The equation contains a diffusion term correspond- of gravity. We highlight the parameters and select case ing to random cell movement, a nonlocal dispersion term studies where memory changes the vertical and horizontal corresponding to cell-cell adhesion, a cell age dependent transport. boundary condition corresponding to cell division, and a nonlinear logistic term corresponding to constrained popu- Ksenia Guseva lation growth. Basic properties of the solutions are proved, University of Oldenburg, Theoretical Physics/Complex including existence, uniqueness, positivity, and long-term Systems behavior dependent on parametric input. The model is Oldenburg, Germany illustrated by simulations applicable to in vitro wound clo- [email protected] sure experiments, which are widely used for experimental testing of cancer therapies. Ulrike Feudel University of Oldenburg Glenn Webb ICBM, Theoretical Physics/Complex Systems Department of Mathematics [email protected] Vanderbilt University [email protected] Tamas Tel E¨otv¨os Lor´and University, Budapest, Hungary Institute for Theoretical Physics MS34 [email protected] Mathematical Models of the Treatment of Chronic Lymphocytic Leukemia with Ibrutinib and the De- velopment of Drug Resistance MS35 Effect of Fluid and Particle Inertia on the Dynam- Chronic lymphocytic leukemia (CLL) is the most common ics and Scaling of Ellipsoidal Particles in Shear leukemia in the western world. A recently developed tar- Flow geted kinase inhibitor, ibrutinib, has shown very promising results in clinical trials and has now been approved for the Simulations of the rotational behaviour of ellipsoidal par- treatment of the disease. I will discuss mathematical mod- ticles in linear shear flow are made by the Lattice Boltz- els that have been used to analyze the dynamics of CLL mann Method. As fluid and/or particle inertia is increased, cells during drug therapy, and show how this model can be a number of rotational states are observed and the bifur- used to estimate parameters and obtain important insights cation sequence is detected and analysed. The behaviour into the mechanisms of action of the drug. Further, I will of triaxial particles will be presented in some detail. It discuss mathematical models that seek to predict the dura- is observed that the drift to chaotic rotation observed in tion for which ibrutinib can maintain control of the disease, creeping flow seems to be less significant with fluid inertia and when drug resistance causes relapse of the disease. present.

Dominik Wodarz Tomas Rosen Dept. of Ecology and Evolutionary Bio KTH Mechanics University of California, Irvine Royal Institute of Technology [email protected] [email protected]

MS35 Yusuke Kotsubo Tokyo University Inertia Effects in the Dynamics of Spherical and [email protected] Non-Spherical Objects at Low Reynolds Number

Particles moving in a fluid at low but finite Reynolds num- Cyrus Aidun bers experience hydrodynamic forces that may be signifi- G.W. Woodruff School of Mechanical Engineering cantly affected by fluid inertia. As a result the particle dy- Georgia Institute of Technology namics (both translational and rotational) may be strongly [email protected] altered. This presentation aims at presenting theoretical tools, essentially based on matched asymptotic expansions, Fredrik Lundell which allow to take these effects into account in certain sit- KTH Stockholm uations. Sweden [email protected] Fabien Candelier Aix-Marseille University France MS35 [email protected] The Effect of Particle and Fluid Inertia on the Dy- namics of Particles in Flows

MS35 The dynamics of a very small particle suspended in a fluid Influence of the History Force on Inertial Parti- flow is simple: the centre-of-mass is advected by the fluid cle Advection: Gravitational Effects and Horizon- velocity, and the orientational dynamics is determined by DS15 Abstracts 143

the sequence of fluid-velocity gradients that the particle ex- tem to absorb disturbance and still retain its structure and periences. For larger particles inertial effects may become function. This ecologically and socially relevant definition important. Particle inertia is relatively straightforward to of resilience is used in ecology, medicine, and climate sci- treat and there has recently been substantial progress in ence, and by policy makers in community, government and understanding its effect upon the dynamics of particles in conservation efforts. Despite this fast growing interest in flows. The effect of fluid inertia, by contrast, is more dif- resilience across the sciences and social sciences, there is ficult to describe. In this talk I will review what is known little work done to describe resilience in quantifiable math- about the effect of fluid inertia upon the translational and ematical terms. The Resilience Focus Group of the Mathe- orientational motion of particles in flows. matics and Climate Research Network is working on quan- tifiable definitions of resilience. A continuous dynamical Bernhard Mehlig system is used to model the undisturbed ecological or bio- Gothenburg Univ logical system, but what kind of perturbations best model Gothenburg, Sweden disturbance to the system? How is resilience different from [email protected] Lyaponov stability of the system? What metrics could we use to understand this difference?

MS36 Alanna Hoyer-Leitzel How Nonsmooth Are the Earth Sciences? Mathematics Department Bowdoin College Geological folding of sedimentary rock layers is often [email protected] thought of as being a smooth process, leading to regular si- nusoidal folds. In fact, a look at actual rocks will show you that they often fold in a different non-smooth manner, with MS36 sharp corners. Such folding patterns include kink bands and (zig-zag) chevron folds. Non-smooth features are of- The Search for Glacial Cycles: A Quasiperiodi- ten linked to the presence of (possibly precious) minerals cally Forced Nonsmooth System in a Conceptual deep underground. In this talk I will develop a theory for Climate Model such non-smooth behaviour which accounts for the friction and compression between rock layers. This theory gives a The glacial-interglacial cycle provides mesmerizing dynam- consistent description of the non-smooth folding patterns ical system and modeling topics. We present a novel en- in terms of novel homoclinic bifurcations. ergy balance model with glacial mass balance adjustment. The model is a non-smooth dynamical system with non- Chris Budd autonomous orbital forcing, exhibiting a similar sawtooth Dept. of Mathematical Sciences result typical of glacial and interglacial cycles. Some future University of Bath, UK dynamical challenges will be outlined. [email protected] Esther Widiasih Tim J. Dodwell Mathematics and Science Subdivision Bath Institute of Complex System University of Hawai‘i West O‘ahu [email protected] [email protected]

James Walsh MS36 Oberlin College Analysis of an Arctic Sea Ice Model in a Nons- [email protected] mooth Limit Richard McGehee, Jonathan Hahn We analyze an energy balance model for the Arctic, which University of Minnesota takes the form of a low-dimensional, periodically forced dy- [email protected], [email protected] namical system that captures key feedbacks, in the limit of discontinuous ice-albedo feedback. This mathematical simplification enables detailed analysis and provides intu- MS37 ition for the role that the discontinuity boundary in phase space plays in the bifurcation structure of the model. We Probabilistic Approach to Deployment Strategy in explore how this analysis provides an alternative perspec- Lagrangian Data Assimilation tive on previous numerical studies of this model. A sequence of position observations by Lagrangian instru- Kaitlin Hill ments, such as drifters and floats, contains time-integrated Engineering Sciences and Applied Mathematics information of local flow velocity along the trajectories. Northwestern University Direct assimilation of these Lagrangian observations is ef- [email protected] fective in estimating time-evolving, underlying flow. Along a trajectory, each observation has a limited region of influ- Mary Silber ence where dynamic correlation to the observation location Northwestern University is significant. Because trajectories are governed by the La- Dept. of Engineering Sciences and Applied Mathematics grangian geometry of the underlying flow, design of the [email protected] deployment strategy should take into account the detec- tion of the Lagrangian geometry. However, even when the underlying flow is perfectly known, detection of the La- MS36 grangian geometry is challenging. In this talk, we present Mathematical Quantifications of Resilience a probabilistic approach to Lagrangian data assimilation that incorporates the detection of the Lagrangian geom- Roughly speaking, resilience refers to the capacity of a sys- etry while estimating the underlying flow and design the 144 DS15 Abstracts

deployment strategy accordingly. setting. Bayesian nonlinear adaptive sampling schemes are then derived to predict the observations to be collected Kayo Ide that maximize the mutual information about variables of Dept. of Atmospheric and Oceanic Sciences interest. Examples are provided for fluid and ocean flows. University of Maryland, College Park This is joint work with our MSEAS group at MIT. [email protected] Tapovan Lolla, Pierre Lermusiaux MIT MS37 [email protected], [email protected] A Quantitative Measure of Observability for Data Assimilations MS38 For complicated systems found in numerical weather pre- A 3D Model of Cell Signal Transduction diction, we introduce a characterization of observability to quantify the quality of information provided by sensors and We consider a 3D model of cell signal transduction in which prior knowledge. Optimal sensor positions can be found by the enzymes promoting the various stages in the signal are maximizing the observability. To evaluate the performance in fixed positions within the cell. We use the method of of this method we consider the assimilation sensitivity of matched asymptotic expansions to reduce the partial dif- the optimized sensors as well as the performance in Monte ferential equation modeling the signal transduction process Carlo experiments against test cases. Lastly we discuss the to a system of ordinary differential equations. We consider application of the method to mobile sensors. various bifurcations and the addition of delay to the sys- tem. Wei Kang Naval Postgraduate School David Iron Department of Applied Mathematics Dalhousie University, Canada [email protected] [email protected]

Sarah King, Liang Xu MS38 Naval Research Laboratory Organization of Metabolic Reactions for Improved [email protected], Efficiency: Carbon Fixation and Bioengineering [email protected] Applications Recent advances in the experimental understanding of cel- MS37 lular organization motivate the need for novel spatial mod- Multivehicle Motion Planning in the Presence of eling of reactions in cells. Cells organize biochemical reac- Ocean Eddies tions to optimize growth, prevent toxic side-reactions, and direct metabolic flux. We review recent experimental work, We present a path-planning paradigm for a team of au- traditional methods for modeling metabolic networks, and tonomous sampling platforms in the presence of coherent open problems. We present an example model of how the ocean eddies. Vehicle paths near eddies are planned by organization of carbon fixation reactions in photosynthetic utilizing Hamiltonian dynamics with added dissipation to bacteria improves reaction efficiency reducing the energy generate control vector fields for vehicle guidance. The needed for growth of cells. path-planning framework is based on the concept of an ac- tive singularity whose strength is a tunable control input. Niall M. Mangan The active singularities are associated with individual ve- Massachusetts Institute of Technology hicles and the Hamiltonian structure of their dynamics en- [email protected] ables a principled method for motion planning.

Frank D. Lagor MS38 University of Maryland An Spatial Model of Anti-Cancer Drug Resistance: Department of Aerospace Engineering theRoleoftheMicro-Environment fl[email protected] Although resistance to chemotherapeutic agents seems to Derek A. Paley be bound to appear, it is difficult to determine whether it University of Maryland arises prior to, or as a result of, cancer therapy. We devel- Dept. Aerospace Engineering and Inst. for Systems oped a hybrid discrete-continuous mathematical model to Research explore anti-cancer drug resistance development. We de- [email protected] scribe cells through a particle-spring approach responding to changing levels of oxygen and drug concentrations, us- ing partial differential equations. We consider two kinds of MS37 resistance (namely pre-existing and acquired) and explore Bayesian Nonlinear Smoothing and Mutual Infor- the role of microenvironmental niches of drug and oxygen mation for Adaptive Sampling intumorcellsurvivalandtumorexpansion.

New schemes are presented for optimal Bayesian nonlin- Kerri-Ann Norton ear state estimation and adaptive sampling of nonlinear Johns Hopkins University fluid and ocean dynamical systems, both forward and back- Department of Biomedical Engineering ward in time. The Bayesian nonlinear smoothing com- [email protected] bines reduced-order Dynamically-Orthogonal (DO) equa- tions with Gaussian Mixture Models (GMMs), extending Kasia Rejniak linearized backward pass updates to a Bayesian nonlinear H. Lee Moffitt Cancer Center & Research Institute DS15 Abstracts 145

Integrated Mathematical Oncology attractors are outlined. kasia.rejniak@moffitt.org Denis Blackmore Jana Gevertz New Jersey Institute of Technology The College of New Jersey Newark, NJ 07102, USA [email protected] [email protected]

Judith P´erez-Vel´azquez Anthony Rosato Helmholtz Zentrum M¨unchen New Jersey Institute of Technology Institute of Computational Biology Newark, NJ 07102, USA [email protected] [email protected]

Zahra Aminzare Hao Wu Rutgers university New Jersey Institute of Technology [email protected] Newark, NJ 07102 USA [email protected] Alexandria Volkening Brown University MS39 alexandria [email protected] Collective Coordinates as Model Reduction for Nonlinear Wave Interactions

MS38 The linear superposition of two traveling wave solutions of Synthetic Genetic Circuits for Spatial Patterning a PDE offers a quantitative description of nonlinear wave interactions, provided certain parameters, usually termed One promise of synthetic biology is the creation of genetic “collective coordinates”, of the shapes (e.g., the trajecto- circuitry that enables the execution of logical programming ries of the centers) are considered unknown a priori. For in living cells. Our lab has previously engineered intracel- PDEs with Hamiltonian structure, substituting such an lular and multicellular oscillators that give robust dynamic ansatz into the Lagrangian leads to a reduced-order dy- behavior and observed them at the single cell and colony namical model (a “coarse-grain” description) in the form level using time-lapse microscopy. We have recently turned of (a few) coupled nonlinear ODEs. To demonstrate the to the task of creating a circuit giving robust spatial oscil- versatility of this variational technique, the sine–Gordon ∗ lations of gene expression in a population – stripes. The wave and the K (l, p) evolution equations are considered. key to robust oscillations in temporal genetic oscillators was positive feedback coupled to delayed negative feed- Ivan C. Christov back. In the spatial case, time delay corresponds to spatial Los Alamos National Laboratory offset, suggesting that stripe formation will require local [email protected] positive feedback coupled to long-range negative feedback. This is essentially the model of pattern formation first de- scribed by Turing and expanded on by Gierer and Mein- MS39 hardt. These models as originally formulated require two On the Calogero Type Integrable Discretization of signals diffusing at very different rates, but similar pat- Nonlinear Dynamical Systems terning mechanisms can function even if the two signals diffuse at the same rate. Signals that do not crosstalk are The Calogero type matrix discretization scheme is applied required for these patterning mechanisms, but orthogonal to constructing Lax type integrable discretizations of non- signals for synthetic genetic circuits have proved elusive. linear dynamical systems. The Lie-algebraic integrability Recently we have developed a system that permits two sig- properties of co-adjoint flows on the related Markov type nals to be used in the same cell and her we describe efforts Lie algebras are discussed. to construct self-organizing genetic circuits using this new tool. Anatolij Prykarpatski AGH University of Science and Technology Paul Steiner 30-059 Krakow, Poland University California San Diego [email protected] San Diego, CA USA [email protected] MS39 A Scheme for Modeling and Analyzing the Dynam- MS39 ics of Logical Circuits Reduced Models for Granular and Ecological Dy- It is shown how logical circuits can be modeled by discrete namics dynamical systems. While continuous dynamical systems provide quite accurate mechanistic models, they tend to be The potency of reduced dynamical models is illustrated computationally expensive to simulate. In contrast, sim- with two examples: First, by a sequence of reductions from ulating a discrete dynamical system is relatively inexpen- infinite-dimensional to discrete dynamical models of gran- sive. A model for the RS flip-flop circuit is constructed ular flows. The effectiveness of these models for predicting using chaotic NOR gates. Next, a systematic - algorith- granular dynamics is demonstrated, as are some innovative mic - first principles approach is developed and shown to integrability results they have inspired. Secondly, effective be useful in obtaining models of more complicated logical reduced discrete dynamical models for ecological dynamics circuits. are described and analyzed, and some associated serendip- itous insights on the identification and analysis of strange Aminur Rahman 146 DS15 Abstracts

New Jersey Institute of Technology Bjorn Sandstede [email protected] Division of Applied Mathematics Brown University bjorn [email protected] MS40 Predator-Swarm Interactions Mads Peter Soerensen Department of Mathematics We propose a minimal model of predator-swarm interac- Technical University of Denmark tions which captures many of the essential dynamics ob- [email protected] served in nature. Different outcomes are observed depend- ing on the predator strength. For a weak predator, the Jens Starke swarm is able to escape the predator completely. As the Technical University of Denmark strength is increased, the predator is able to catch up with Department of Mathematics the swarm as a whole, but the individual prey is able to es- [email protected] cape by confusing the predator: the prey forms a ring with the predator at the centre. For higher predator strength, complex chasing dynamics are observed which can become MS40 chaotic, and eventually leading to successful prey capture. Topological Data Analysis of Biological Aggrega- Our model is simple enough to be amenable to a full math- tion Models ematical analysis, which is used to predict the shape of the swarm as well as the resulting predatorprey dynamics as a We apply tools from topological data analysis to two math- function of model parameters. The complex shape of the ematical models inspired by biological aggregations such swarm in our model during the chasing dynamics is similar as bird flocks, fish schools, and insect swarms. Our data to the shape of a flock of sheep avoiding a shepherd. consists of numerical simulation output from the models of Vicsek, et al. and D’Orsogna, et al.. These models Theodore Kolokolnikov are dynamical systems describing the movement of agents Dalhousie University who interact via alignment, attraction, and/or repulsion. [email protected] Each simulation time frame is a point cloud in position- velocity space. We analyze the topological structure of MS40 these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti Non-Standard Travelling Waves in Traffic and numbers count connected components, topological circles, Pedestrian Flow Models and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti Non-standard waves for particle models of car traffic and numbers over simulation time and topological persistence pedestrian flow are presented and analyzed both analyt- scale. We compare our topological results to order param- ically and numerically. The car traffic model is an ex- eters typically used to quantify the global behavior of ag- tended optimal velocity model with velocity dependent gregations, such as polarization and angular momentum. driver strategies which shows traveling multi-pulse traf- The topological calculations reveal events and structure fic jams and modulated waves. The pedestrian model is not captured by the order parameters. based on a social force model with asymmetric couplings (pedestrians in front have bigger influence on the pedes- Chad M. Topaz trian behaviour) and shows transitions to multi-lane waves Macalester College and peristaltic motion. [email protected] Paul Carter Division of Applied Mathematics Lori Ziegelmeier, Tom Halverson Brown University Dept. of Mathematics, Statistics, and Computer Science paul [email protected] Macalester College [email protected], [email protected] Peter Leth Christiansen Department of Applied Mathematics and Computer MS40 Science Technical University of Denmark Modeling Stripe Formation in Zebrafish [email protected] Zebrafish is a small fish with distinctive black and yel- low stripes that form due to the interaction of different Yuri Gaididei pigment cells. We present a comprehensive agent-based Bogolyubov Institute for Theoretical Physics model for stripe formation in zebrafish that describes the Kiev full spectrum of biological data: development from a larval [email protected] pre-pattern, ablation experiments, and mutations. We find that fish growth shortens the necessary scale for long-range Carlos Gorria interactions and that iridophores, a third type of pigment Department of Applied Mathematics and Statistics cell, maintain stripe boundary integrity. University of the Basque Country [email protected] Alexandria Volkening Brown University Christian Marschler alexandria [email protected] Technical University of Denmark Department of Mathematics and Computer Science Bjorn Sandstede [email protected] Division of Applied Mathematics DS15 Abstracts 147

Brown University Institute of Industrial Science bjorn [email protected] The University of Tokyo [email protected]

MS41 Kazuyuki Aihara Stability of Power Grid: Dynamical Systems Per- JST/University of Tokyo, Japan spective Dept of Mathematical Sciences [email protected] Power grids can be conveniently represented as dynamical systems. Their normal operations depend on two kinds of Hideyuki Suzuki stability: steady state and transient stability. An overview University of Tokyo of the techniques for estimation of both types of stability [email protected] will be given. An approach for improving the stability based on using electrical vehicles plugged to the grid will be presented. Influence of the delays on the stabilization MS41 will be also shown. Hierarchical Subsystem Clustering for Distributed Andrej Gajduk Control of Networked Systems Macedonian Academy of Sciences and Arts, Skopje, We examine hierarchical subsystem clustering for net- Macedonia worked systems in the framework of hierarchical dis- [email protected] tributed control proposed by the authors. More specifi- cally, for various existing clustering methods such as the Mirko Todorovski K-means method, we numerically examine stability as well Ss Cyril and Methodius University, Faculty of electrical as control performance of the whole control system with eng resultant subsystem clusters. This study is expected to be [email protected] a first step towards development of hierarchical distributed control theory with systematic determination of subsystem Lasko Basnarkov clustering. Macedonian Academy of Sciences and Arts [email protected] Tomonori Sadamoto, Takayuki Ishizaki, Jun-ichi Imura Tokyo Institute of Technology Ljupco Kocarev [email protected], [email protected], University of California, San Diego [email protected] Institute for Nonlinear Science [email protected] MS42 On the Relationship Between Koopman Mode De- MS41 composition and Dynamic Mode Decomposition Analysis of Systems in Buildings Using Koopman We present an explicit relationship between Koopman Operator Methods Mode Decomposition (KMD) of dynamical systems and Commercial buildings consume 20% of U.S. energy half companion-matrix version of Dynamic Mode Decomposi- of which is due to Heating, Ventilation, & Air Condition- tion (DMD). We use this relationship to explain some of the ing. Due to the multiple time-scales and spatial configu- differences in the variants of DMD algorithm. We also dis- rations of HVAC sub-systems, energy efficiency is difficult cuss some applications of DMD as a tool to extract Koop- to achieve. By projecting building time-series data onto man modes from experimental and computational data. eigenmodes of the Koopman operator, interactions between Hassan Arbabi sub-systems become identifiable leading to improved build- UC Santa Barbara ing performance. Technique is illustrated on model simu- [email protected] lated predictions and actual sensor data.

Michael Georgescu Igor Mezic University of California, Santa Barbara University of California, Santa Barbara [email protected] [email protected]

MS41 MS42 Time Series Prediction for Renewable Energy Re- Extracting Spatial-Temporal Coherent Patterns in sources Large-Scale Neural Recordings Using Dynamic Mode Decomposition The prediction of renewable energy outputs is almost equivalent to weather forecasting, although the time reso- There is a broad need in the neuroscience community to lutions often required are different between these two: the understand and visualize large-scale recordings of neural prediction of renewable energy often needs the finer reso- activity, big data acquired by tens or hundreds of electrodes lution that can go down to the orders of seconds and min- simultaneously recording dynamic brain activity over min- utes. The prediction of renewable energy outputs of such utes to hours. Such dynamic datasets are characterized by a finer resolution can be realized by employing time series coherent patterns across both space and time, yet existing prediction with empirical observations rather than refining computational methods are typically restricted to analy- outputs of global circulation models. sis either in space or in time separately. Here we report the adaptation of dynamic mode decomposition (DMD), Yoshito Hirata an algorithm originally developed for the study of fluid 148 DS15 Abstracts

physics, to large-scale neuronal recordings. We validated tronic circuits, while considering many crucial component the DMD approach on sub-dural electrode array recordings design limitations such as frequency response, bandwidth, from human subjects performing a known motor activation noise, linearity and parasitics. task. Next, we leveraged DMD in combination with ma- chine learning to develop a novel method to extract sleep Aubrey N. Beal, Robert Dean spindle networks from the same subjects. We suggest that Auburn University DMD is generally applicable as a powerful method in the [email protected], [email protected] analysis and understanding of large-scale recordings of neu- ral activity. MS43 Bing W. Brunton A Pseudo-Matched Filter for Solvable Chaos University of Washington [email protected] In the work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic waveforms pro- duced by a piecewise-linear dynamical system. Motivated MS42 by these results, we systematically investigate the matched Dynamic Mode Decomposition with Control with filters properties in order to design a pseudo-matched fil- a Special Focus on Epidemiological Applications ter, which captures important features of the matched fil- ter and is realized using first order filters. Using numerical Here, we present a new method called Dynamic Mode De- simulations and statistical analyses, we compare the per- composition with control (DMDc) which, similar to Dy- formances of the matched and pseudo-matched filters. namic Mode Decomposition (DMD), finds low-order mod- els from high-dimensional, complex systems, but now in- Seth D. Cohen corporates the effect of external control. In contrast to Ducommun Miltec DMD, DMDc is capable of producing an accurate input- Huntsville, AL output model recovering the dynamics and modes without [email protected] being corrupted by external forcing. We focus on a set of epidemiological applications which have both dynamics and interventions (control). MS43 Joshua L. Proctor Communication Waveforms and Exactly Solvable Intellectual Ventures Chaos [email protected] We show that, under practical constraints, an optimal com- munication waveform is chaotic. That is, we assume a MS42 simple matched filter and derive the corresponding basis function that maximizes the receiver signal-to-noise per- A Rigorous Definition and Theory of Dynamic formance. We then consider a communication waveform Mode Decomposition using this basis function, and surprisingly we find a wave- Dynamic mode decomposition (DMD) is often described form return map that is conjugate to a chaotic shift map. algorithmically, rather than through a set of defining math- We also show a relationship of the optimal waveform to ematical properties, as other decompositions are. In this an exactly solvable hybrid chaotic oscillator that has been talk, we present a formal definition of DMD that agrees previously reported. with the familiar algorithmic descriptions. This establishes a foundation from which new theory and algorithms can Ned J. Corron be developed. For instance, it allows for non-sequential U.S. Army RDECOM datasets and elucidates the connections between DMD, [email protected] Koopman operator theory, the eigensystem realization al- gorithm, and linear inverse modeling. Jonathan N. Blakely US Army RDECOM Jonathan H. Tu [email protected] UC Berkeley [email protected] MS43 Clarence Rowley Exactly Solvable Chaos in An Electromechanical Princeton University Oscillator Department of Mechanical and Aerospace Engineering [email protected] A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that MS43 include a linear second order ordinary differential equa- Methods for Implementing Exactly Solvable Chaos tion with negative damping and a discrete switching con- in Electronic Circuits dition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological Exactly solvable chaos may lend many advantages to ap- structure similar to either the Lorenz butterfly or R¨ossler’s plications in radar, communications, computing and secu- folded-band oscillator depending on the configuration. Ex- rity. In order for these technologies to benefit from the use act solutions are written as a linear convolution of a fixed of exactly solvable chaos, these governing equations must basis pulse and a sequence of discrete symbols. We find be first implemented using various electronic circuit de- close agreement between the exact analytical solutions and sign techniques. This work outlines various methodologies the physical oscillations. Waveform return maps for both for realizing exactly solvable chaos using mixed-signal elec- configurations show equivalence to either a shift map or DS15 Abstracts 149

tent map, proving the chaotic nature of the oscillations. Gary Froyland UNSW Australia Lucas Illing [email protected] Reed College [email protected] Anthony Quas University of Victoria MS44 [email protected] A Measurable Perspective on Finite Time Coher- ence MS44 The concept of coherent structures in a flow refers to no- On Triangularization of Matrix Cocycles in the tions of subsets of the flow which preserve some measurable Multiplicative Ergodic Theorem quantity, despite the generally nonlinear flow: something simple embedded in the complexity. Our own perspective The Multiplicative Ergodic Theorem shows that a real ma- of shape coherent sets is defined in terms of flow that is trix cocycle is block diagonalizable over the real numbers, locally as rigid body motions, and uncovered by investi- given mild hypotheses; that is, the cocycle is cohomologous gating boundary curvature evolution. Key for unifying to to one in which the matrices are supported on blocks corre- other concepts of coherence is choice of measure interpreted sponding to the Lyapunov exponents. We shall talk about across domains . block triangularizing cocycles, and investigate when this may occur; namely, not all cocycles may be triangularized, Erik Bollt even over the complex numbers. Clarkson University [email protected] Joseph Horan Department of Mathematics and Statistics University of Victoria Tian Ma [email protected] Department of Mathematics and Computer Science Clarkson University [email protected] MS45 Vibration Energy Harvesting Based on Nonlinear MS44 Targeted Energy Transfer Rigorous Numerical Approximation of Invariant We investigate the use of targeted energy transfer via es- Measures – History and Recent Progress sential (nonlinearizable) stiffness nonlinearity to promote Interest in rigorous schemes to approximate invariant mea- efficient energy harvesting. The system of interest consists sures in ergodic theory dates back at least to Ulam’s cel- of two oscillators, a linear primary and strongly nonlinear ebrated 1960 conjecture about their approximation via secondary, coupled electromechanically. The primary is a finite-dimensional Markov chains. We review this history grounded linear oscillator; the secondary, the harvester, from the modern perspective of spectral perturbation. Re- is a lightweight oscillating mass attached to the primary cently, with R. Murray, convex optimization techniques mass through a permanent magnet, inductance coil, and have been proposed; we compare and contrast these with untensioned steel wire positioned normal to the direction Ulam’s scheme. Finally, we place all of these approaches of the oscillation, which provides the purely cubic essential into a unified setting of regularized least-squares optimiza- nonlinearity. Impulsive excitation of the primary at a suf- tion for solution of the (ill-posed) Perron-Frobenius fixed ficiently high level results in transient resonance capture point problem. with the secondary, resulting in a large-amplitude high- frequency component in the harvester response. Energy Chris Bose generated is harvested in a circuit via the magnet and coil. Mathematics and Statistics Performance is demonstrated through both simulation and University of Victoria, Canada experiment. [email protected] Kevin Remick Department of Mechanical Science and Engineering MS44 University of Illinois - Urbana- Champaign Non-Autonomous Dynamical Systems, Multiplica- [email protected] tive Ergodic Theorems and Applications D Dane Quinn Non-autonomous dynamical systems yield very flexible University of Akron models for the study of time-dependent systems, with driv- Dept of Mechanical Engineering ing mechanisms ranging from deterministic forcing to sta- [email protected] tionary noise. Multiplicative ergodic theorems (METs) en- compass fundamental information for the study of trans- D. Michael McFarland port phenomena in such systems, including Lyapunov ex- University of Illinois ponents, invariant measures and coherent structures. In [email protected] this talk, we will discuss recent developments on METs, motivated by questions coming from oceanic and atmo- spheric dynamics. Lawrence Bergman University of Illinois - Urbana - Champaign Cecilia Gonzalez Tokman [email protected] School of Mathematics and Statistics University of New South Wales Alexander Vakakis [email protected] University of Illinois 150 DS15 Abstracts

[email protected] [email protected]

MS45 MS46 The Effect of Extrinsic Noise on Gene Regulation Nonlinear Energy Harvesting in Granular Media Stochastic gene expression is influenced both by intrinsic In this talk, we explore the possibility of using granular noise (IN) arising from intracellular variability and extrin- crystals for the purpose of vibration energy harvesting. sic noise (EN) arising from intercellular variability. While In particular, we focus on time-periodic structures of such IN is well understood, a rigorous understanding of how EN systems and how the interplay of spatial heterogeneity, dis- influences the function of genetic networks is still lacking. creteness and nonlinearity can lead to desirable localization Here we study the IN/EN interplay in simple network mo- properties. We approach the problem with computational, tifs, focusing of how EN characteristics affect the overall analytical and experimental tools. statistics. Our analytical predictions are compared with Monte-Carlo simulations efficiently accounting for fluctu- ating reaction rates. Christopher Chong ETH Zurich Michael Assaf [email protected] Racah Institute of Physics Hebrew University of Jerusalem [email protected] MS45 2D Energy Channeling in the Locally Resonant MS46 Acoustic Metamaterials Fundamental Limits to the Precision of Multicellu- lar Sensing Dynamics of locally resonant, acoustic meta-materials is a subject of intense study of the past few years. As of today Single cells sense their environment with remarkable pre- there is a lack of a substantial theoretical understanding cision. At the same time, cells communicate. How are of the dynamics of locally resonant, 1D, 2D non-linear lat- sensing and communication related? I will describe a sys- tices. In the present talk I’ll present the recent results of tem in which epithelial cells, by communicating, can detect the theoretical study of controlled, unidirectional energy shallower chemical gradients than single cells can alone. A transport, wave redirection and nonlinear energy channel- minimal stochastic model provides fundamental limits on ing in the locally resonant, 2D metamaterials, incorporat- the precision of communication-aided sensing, which we ing internal rotators. validate in the experimental system. Our results demon- strate that known sensory limits are altered when commu- Yuli Starosvetsky nication is accounted for. Technion, Israel Institute of Technology Andrew Mugler [email protected] Department of Physics and Astronomy Purdue University Kirill Vorotnikov [email protected] Faculty of Mechanical Engineering Technion - Israel Institute of Technology Matthew Brennan [email protected] Johns Hopkins University [email protected]

MS45 Andre Levchenko Non-Linearizable Wave Equation: Nonlinear Sonic Yale University Vacuum [email protected] Ilya Nemenman We consider low-energy oscillations of a finite spring-mass Emory University chain in the plane, with geometric nonlinearity generating [email protected] a smooth nonlinear sonic vacuum with zero speed of sound, and strongly non-local nonlinear terms despite only next- neighbor physical interactions between particles. The non- MS46 linear normal modes of this system are identical to those of a simple linear spring-mass chain. Asymptotic analy- Inferring Predictive Signal-Activated Gene Regu- sis reveals a rich structure of resonance manifolds, mixed lation Models from Noisy Single-Cell Data standing/traveling waves, and strong nonlinear energy ex- changes between modes. Spatial, temporal and stochastic fluctuations can cause ge- netically identical cells to exhibit wildly different behav- iors. At first glance, fluctuations seem to compromise cel- Leonid Manevich lular responses, complicate modeling, and disrupt predic- Semenov Institute of Chemical Physics tive understanding and control. Under closer examination, Russian Academy of Sciences cellular fluctuations actually become exceptionally useful. [email protected] I will discuss how integrating single-cell experiments with precise spatiotemporal stochastic analyses can reveal new Alexander Vakakis insight, enable quantitatively predictive models, and im- University of Illinois prove the controllability of heterogeneous gene regulation DS15 Abstracts 151

in bacteria, yeast and mammalian systems. [email protected]

Brian Munsky College of Engineering MS47 Colorado State University Generalized Laplace Analysis and Spaces of Ob- [email protected] servables for the Koopman Operator

We extend Koopman spectral analysis to spectral operators MS46 of scalar type having non-unimodular spectrum and give Coarse-Graining Biochemical Networks conditions on the spectrum so that spectral projections can be computed using Laplace averages. This naturally ex- We consider a generic stochastic model either for ion trans- tends the theory existing for dynamical systems restricted port through a single channel with arbitrary internal struc- to an attractor, where spectral projections are computed ture or arbitrary enzyme kinetics. We show that mea- using Fourier averages, to dissipative systems. For dynam- surements of statistics of transition times through specific ical systems with dissipation, we construct a natural space states of such a system contain only restricted informa- of observables for which the associated Koopman operator tion about parameters of the model. This observation al- is spectral. lows one to identify the most relevant variables that can be quickly estimated if statistical measurements are per- Ryan Mohr formed on a biochemical process at a single molecule level. University of California, Santa Barbara For example, we show that the Poisson indicator in enzyme [email protected] kinetics depends only on three parameters in addition to the parameters of the Michaelis-Menten curve that charac- terizes average enzyme turnover rate in a very broad class MS47 of enzyme models. Nevertheless, measurement of Poisson What Can the Koopman Operator Do for Dynam- indicator or Fano factor for such renewal processes can dis- ical Systems? criminate reactions with multiple intermediate steps as well as provide valuable information about the internal kinetic We report on ”Operator Theoretic Aspects of Ergodic The- rates. ory” as developed in the new monograph with the same name (Springer 2015, coauthored by Tanja Eisner, Balint Nikolai Sinitsyn Farkas, Markus Haase and R.N.) and their applications to Theoretical division nonlinear dynamical systems. Los Alamos National Laboratory [email protected] Rainer Nagel University of Tubingen [email protected] MS47 Computation of the Koopman Eigenfunctions Is a Systematic Method for Global Stability Analysis MS48 An Observational Basis for Sudden Stratospheric The Koopman operator framework provides a novel ap- Warmings As Bifurcations in Planetary Wave Am- proach to global stability analysis of dynamical systems, plitude which can be seen as an extension of classic stablility analy- sis of linear systems. We show that the existence of specific Sudden stratospheric warmings (SSWs) are midwinter eigenfunctions of the operator is a necessary and sufficient events in which the polar cap temperature and circulation condition for global stability of the attractor. Moreover, undergo large and abrupt changes. Currently two compet- the computation of the eigenfunctions in a polynomial ba- ing theories contend to explain the explosive stratospheric sis yields systematic methods for stability analysis and es- wave amplitude growth that triggers a SSW: anomalously timation of the basin of attraction. large planetary wave forcing, or nonlinear resonance. In this work we utilize 35 years of atmospheric data to show Alexandre Mauroy, Igor Mezic that SSWs are most likely triggered by a wave amplitude University of California, Santa Barbara bifurcation due to nonlinear resonance. [email protected], [email protected] John R. Albers CIRES, University of Colorado MS47 NOAA/ESRL Phys. Sci. Division Koopman Mode Expansion in Theory and Practice [email protected]

We discuss current theory and practice of applications of Koopman operator methods in dynamical systems and its MS48 relationship with computational methods. The approach Tropical-Extratropical Wave Interactions in the has recently been extended to associate geometrical ob- Atmosphere jects such as isochrons and isostables with level sets of Koopman eigenfunctions. We will also discuss the relation- The coupling between moist convective processes and large- ship between numerical methods such as Dynamic Mode scale circulation is at the core of tropical-extratropical at- Decomposition and Koopman Mode Decomposition, and mospheric interactions. Observational evidence of this type extensions of theory to stability of nonlinear systems and of phenomena will be presented and a reduced model will control. be proposed to understand the physical processes underly- ing this type of multi-scale interactions. In particular, the Igor Mezic model will be used to interpret the relative roles of trop- University of California, Santa Barbara ical versus extratropical wave sources of moist convection 152 DS15 Abstracts

modulations at low latitudes. [email protected]

Juliana Dias Arindam Saha NOAA Earth System Research Laboratory IISER Kolkata, India [email protected] [email protected]

MS48 Viktor Avrutin The Use of Green Functions of the Shallow Water IPVS Model for Understanding Climate Anomalies University of Stuttgart [email protected] Climate anomalies are frequently connected the intensity and positioning of anomalous tropical heat sources. Green Laura Gardini Functions of simplified atmospheric models constitute a University of Urbino simple tool for identifying the origin of major climate Department of Economics, Society and Politics anomalies. Examples will be shown for the 2014 climate [email protected] anomalies such as the North American extreme cold period, the flooding in western Europe and the warm conditions in eastern Europe, and the extreme drought in Southeastern MS49 South America that caused severe water shortage. Generalized Hopf Bifurcation in a Nonsmooth Climte Model Pedro Leite da Silva Dias Laboratorio Nacional de Computacao Cientifica, Brazil Low dimensional ocean circulation box models have been IAG, University of Sao Paulo, Brazil used by many scientists to model large scale behavior in [email protected] ocean dynamics. The convection box model we will dis- cuss in this talk exhibits oscillitory behavior, and so was influential to the field at its time of publication. The model MS48 depends on abrupt transitions between two different mixing The Role of Noise in Bifurcations in Fluids and the states, and has a natural nonsmooth limit. In this talk we Atmosphere discuss the Hopf bifurcation in the smooth model, and its continuation to the nonsmooth limit. We will also discuss Triggering the strongest disturbances to the wintertime general forms for this type of nonsmooth Hopf bifurcation. stratospheric polar vortex sudden stratospheric warming (SSWs) is to first order governed by the strength of forcing due to planetary-scale atmospheric waves and the vortexs Julie Leifeld waveguide. Using a model of SSWs, stochastic Kida vortex University of Minnesota equations, we show that the basin of attraction is not only [email protected] more complex than previously believed, but can be signifi- cantly altered by additive noise. Resulting soft bifurcation caused by the random basin is the possible mechanism lead- MS49 ingtoaSSW. Canard Phenomena in Nonsmooth Systems Yuzuru Sato RIES, Hokkaido University This presentation will present new results on canard phe- [email protected] nomena in planar nonsmooth systems. Canard explosion in piecewise-smooth, continuous, planar systems will be David J. Albers discussed, including the super-explosion phenomenon. Ad- Colombia University ditionally, the talk will touch on canard trajectories in dis- Biomedical Informatics continuous systems. It will be shown that it is possible [email protected]. for a discontinuous system to undergo a canard explosion, where part of the stable canard cycle is a Filippov sliding solution. MS49 Andrew Roberts Dangerous Border Collision Bifurcation in Piece- Department of Mathematics wise Smooth Maps The University of North Carolina at Chapel Hill A dangerous bifurcation has been defined as a situation [email protected] where a stable period-1 orbit occurs before and after the bifurcation, and yet the basin of attraction shrinks to zero size at the bifurcation point. It is known that this phe- MS50 nomenon can occur is non-smooth systems. In this paper Intrinsic Mechanisms for Pattern Generation in we generalize the definition to one in which any attract- Three-Node Networks ing orbit may exist before and after the bifurcation, and their basins of attraction shrink to zero size at the bifurca- Bursting patterns can be qualified and modeled using low- tion point, resulting in divergence of orbits starting from dimensional models. We show that, depending on intrin- all initial conditions. Using the normal form of a 2D piece- sic mechanisms of release, escape, and post-inhibitory re- wise smooth map, we develop the conditions and show the bound, reciprocally inhibitory Fitzhugh-Nagumo type net- parameter space regions where this phenomenon occurs. works can produce a range of phase-locked states such as anti-phase bursting, propagating waves, and peristaltic Soumitro Banerjee patterns with recurrently phase-varying lags. Phase-lag Indian Institute of Science education & Research, return maps identify phase states with rhythm switching Kolkata, India and attractor robustness revealed using external inhibition. DS15 Abstracts 153

Our qualification promotes the use of simplified modeling Central Pattern Generators for CPG circuitries.

Jarod Collens We identify and describe the key qualitative rhythmic Georgia State University states in various 3-cell network motifs of a multifunctional Neuroscience Institute and Mathematics Department central pattern generator (CPG). Such CPGs are neural [email protected] microcircuits of cells whose synergetic interactions pro- duce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG Aaron Kelley models, we develop a suite of computational tools that re- GSU duce the problem of stability and existence of rhythmic [email protected] patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincare return maps Deniz Alacam for phase lags between cells. We explore different func- Georgia State University tional possibilities for motifs involving symmetry breaking Mathematics Department and heterogeneity. This is achieved by varying coupling [email protected] properties of the synapses between the cells and studying the qualitative changes in the structure of the correspond- Tingli Xing ing return maps. Our findings provide a systematic basis Georgia State University for understanding plausible biophysical mechanisms for the USA regulation of rhythmic patterns generated by various CPGs [email protected] in the context of motor control such as gait-switching in lo- comotion. Our analysis does not require knowledge of the Drake Knapper equations modeling the system and provides a powerful Georgia State University qualitative approach to studying detailed models of rhyth- [email protected] mic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control. Justus T. Schwabedal Neuroscience Institute Jeremy Wojcik Georgia State University Applied Technology Associates, USA [email protected] [email protected]

Andrey Shilnikov Robert Clewley Neuroscience Institute and Department of Mathematics Georgia State University Georgia State University Department of Mathematics and Statistics, and [email protected] Neuroscience [email protected] MS50 Justus T. Schwabedal From Andronov-Hopf to Z3 Heteroclinic Bifurca- Neuroscience Institute tions in Cpgs Georgia State University [email protected] We study the formation of some rhythmic states in vari- ous 3-cell network motifs of a multifunctional central pat- tern generator (CPG) via several computational tools. Andrey Shilnikov The study is complemented with a detailed analysis of Neuroscience Institute and Department of Mathematics a single leech heart neuron, including bifurcations, spike- Georgia State University counting techniques and Lyapunov exponents, that gives [email protected] a “roadmap” for the basic neuron. We locate a complete route of Andronov-Hopf and heteroclynic cycle connections in the 3-cell leech heart neurons and we illustrate the use MS51 of advanced GPU computing technologies and suitable nu- merical algorithms. Impact of Single-Neuron Dynamics on Transfer of Correlations from Common Input Marcos Rodriguez Centro Universitario de la Defensa [email protected] One source of spike train correlations in the nervous sys- tem is common input, a consequence of the ubiquity of Roberto Barrio, Sergio Serrano coding by populations. The details of how input corre- University of Zaragoza, SPAIN lations map onto output spike correlations is surprisingly [email protected], [email protected] complex, depending on single-neuron dynamics in subtle ways. Much progress has been made in untangling this re- Andrey Shilnikov lationship in Type I and Type II excitable neurons, in both Neuroscience Institute and Department of Mathematics simplified phase oscillator and conductance-based models. Georgia State University In this talk, we apply these techniques to novel patterns of [email protected] excitability that arise in the presence of calcium currents.

Andrea K. Barreiro MS50 Department of Mathematics Key Bifurcations of Bursting Polyrhythms in 3-Cell Southern Methodist University 154 DS15 Abstracts

[email protected] cells project to regular spiking (RS) cells within the bar- rel cortex, as well as to inhibitory cortical fast-spiking (FS) neurons, which in turn project to RS cells. Thus, TC spikes MS51 result in EPSPs followed, with a small time lag, by IPSPs Integrate-and-Fire Model of Insect Olfaction within an RS cell; i.e., the RS cell decodes TC popula- tion synchrony by employing a phase-delayed inhibition When a locust detects an odor, the stimulus triggers a se- synchrony detection scheme. In this work, we construct ries of synchronous oscillations of the neurons in the anten- a biophysical model of a basic ‘building block’ of barrel nal lobe, followed by slow dynamical modulation of the fir- cortex (the feedforward circuit consisting of TC cells, FS ing rates. I model this behavior using an Integrate-and-Fire cells, and a single RS cell) and we examine the role of the neuronal network with excitatory and inhibitory neurons, purely feedforward circuit, and of the phase-delayed inhibi- each with a fast and slow inhibitory conductance response. tion network architecture, in explaining the experimental I derived a coarse-grained model for each (excitatory and data. inhibitory) neuronal population, which allows for more de- tailed analysis of the olfaction mechanisms. Mainak Patel College of William and Mary Pamela B. Fuller [email protected] Rensselaer Polytechnic Institute [email protected] Runjing Liu Duke University Gregor Kovacic [email protected] Rensselaer Polytechnic Inst Dept of Mathematical Sciences Badal Joshi [email protected] California State University, San Marcos [email protected] David Cai Courant Institute for Mathematical Sciences, NYU Shanghai Jiao-Tong University MS52 [email protected] Extending the Zero Derivative Principle

The Zero Derivative Principle determines an approximate MS51 invariant manifold in a singular perturbation systems of A Network of Excitatory and Inhibitory Neurons ODEs by repeated differentiation of the slow components with Gap Junctions of the vector field. We show that even if the slow compo- nents are not identified correctly, an approximate invariant Brain networks are known to give rise to global oscilla- manifold still results from the algorithm, a most useful fea- tions that are linked to synchronized neuronal activity. ture for systems with no explicit time scale separation. We How these oscillations arise is not yet completely under- show results for the Templator, a simple model for a self- stood. Researchers believe that electric coupling through replicating biological system. sites called gap junctions may facilitate their emergence, and determine some of their properties. Following data Morten Brons from experimental papers, we construct a detailed model Technical University Denmark with synaptic and electric coupling for excitatory and in- [email protected] hibitory neurons using a modified version of the Hodgkin Huxley equations. Eric Benot Universite de la Rochelle Jennifer Kile [email protected] Rensselaer Polytechnic Institute [email protected] Mathieu Desroches, Maciej Krupa INRIA Paris-Rocquencourt Gregor Kovacic [email protected], [email protected] Rensselaer Polytechnic Inst Dept of Mathematical Sciences [email protected] MS52 Idealized Models for Vortex Shedding and Fluid- David Cai Body Interactions Courant Institute for Mathematical Sciences, NYU Shanghai Jiao-Tong University The dynamics of free solid bodies in fluids can be in- [email protected] fluenced significantly by vortex shedding. Although this phenomenon depends fundamentally on fluid viscosity, reduced-order models for vortex shedding can be realized MS51 in some cases by imposing velocity constraints on systems Phase Delayed Inhibition and the Representation involving inviscid fluids. Models obtained in this way can of Whisker Deflection Velocity in the Rodent Bar- be framed naturally in the context of geometric mechan- rel Cortex ics and can simplify problems of analysis and control de- sign pertaining to the locomotion of biologically inspired The primary sensory feature represented within the rodent aquatic robots. barrel cortex is the velocity with which a whisker has been deflected. Whisker deflection velocity is encoded within the Scott D. Kelly thalamus via population synchrony (higher deflection ve- Mechanical Engineering and Engineering Science locities entail greater thalamic synchrony). Thalamic (TC) University of North Carolina at Charlotte DS15 Abstracts 155

scott@kellyfish.net [email protected]

MS52 MS53 Ostwald Ripening and Nanoparticle Growth Visualization of Reduced Granular Dynamics Abstract not available. Reduced dynamical models often lend themselves to straightforward plots of the correspond dynamics. Yet, the Martin Rohloff intricate geometry and topology of the resulting phase por- MPI Dynamics and Self-Organization Goettingen trait can prove challenging to convey in a picture. In this martin.rohloff@ds.mpg.de talk, some recent and ongoing work on the visualization of low-dimensional dynamical systems will be discussed. In particular, results obtained for a reduced model of granu- MS53 lar dynamics will be considered. Joint work with D. Black- Episodic Precipitaton more and A. Rosato. Abstract not available. Xavier M. Tricoche J¨urgen Vollmer Purdue University Max Planck Institute for Dynamics and Self-Organization West Lafayette, IN 4707-4348 [email protected] [email protected]

MS54 MS52 Model Free Tuning of Wind Farms for Maximizing A Novel Semidiscete Scheme for a Reduced Con- Power Production tinuum Flow Model In this minisymposium, we introduce our recent result on the model-free approach for maximizing power produc- We focus on numerical methods for solving the BSR equa- tion of wind farms. In particular, by exploiting the spe- tions - a reduced dynamical model for granular and other cial structure of the wind farm about turbines location flows. Using a reliable numerical scheme for the BSR and wind direction, we show our multi-resolution SPSA model, we study the dynamics of a vertically tapped col- based method that can achieve fast model-free controller umn of particles. A novel semi-discrete numerical scheme tuning. Simulation results illustrate that the proposed has been derived to demonstrate the value of BSR models method yields the maximum total power production with for predicting the evolution of granular and other flows. faster convergence compared with other existing model-free Simulation results are compared with experiments and methods. DEM results. Mohd Ashraf Ahmad Hao Wu Department of Systems Science, New Jersey Institute of Technology Graduate School of Informatics, Kyoto University Newark, NJ 07102 USA [email protected] [email protected] Shun-Ichi Azuma Denis Blackmore Kyoto University New Jersey Institute of Technology [email protected] Newark, NJ 07102, USA [email protected] Toshiharu Sugie Department of Systems Science Kyoto University MS53 [email protected] Initiation of Rain and Inertial Particles MS54 Abstract not available. Basin Stability for Evaluating Large Perturbations in Power Grids Markus Abel University of Potsdam The human brain, power grids etc. are all characterized by [email protected] multistability. We claim that the traditional linearization- based approach to stability is often too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of MS53 the basin of attraction which is non-local and easily ap- Aggregate Growth in Optimizing Steel Production plicable, even to high-dimensional systems and apply it to the Northern European power system.

Abstract not available. Juergen Kurths Humboldt Univ,Germany, Potsdam Institute for Climate Nikolas Rimbert Impact Universit´e de Lorraine Research, Germany, and Aberdeen University, UK 156 DS15 Abstracts

[email protected] Princeton University [email protected], [email protected]

MS54 Matthew O. Williams Predicting Critical Links in Complex Supply Net- Program in Applied and Computational Mathematics works Princeton University [email protected] Link failures repeatedly induce large-scale outages in power grids and other complex supply networks. Yet, which links Clarence Rowley are particularly sensitive to inducing such outages is still Princeton University not fully understood. Here we propose two criteria to pre- Department of Mechanical and Aerospace Engineering dict critical links on the basis of the topology of the un- [email protected] damaged network and its load distribution prior to link failure. These criteria outperform critical link prediction based on pure loads or flows more than six-fold. MS55 Marc Timme Parallel Qr Algorithm for Data-Driven Decomposi- NetworkDynamics,MaxPlanckInst.f.Dyn.&Self-Org. tions, in Particular Dynamic Mode Decomposition Goettingen, Germany [email protected] Many fluid flows of engineering applications, although very complex in appearance, can be approximated by lower- Dirk Witthaut order models governed by a few modes, able to capture the Systemforschung und Technologische Entwicklung dominant behavior (dynamics) of the system. Recently, (IEK-STE) different techniques have been developed, designed to ex- Forschungszentrum Julich tract the most dominant coherent structures from the flow. [email protected] Some of the more general techniques are based on data- driven decompositions, most of which rely on performing a singular value decomposition (SVD) on a formulated snap- Martin Rohden shot matrix. As the number of degrees of freedom of a Jacobs University Bremen simulation increases, the resulting data-matrix becomes [email protected] longer, otherwise referred to as a tall-and-skinny (TS) ma- trix. Ultimately, the SVD of a TS data-matrix can no Xiaozhu Zhang, Sarah Hallerberg longer be handled on a single processor. To overcome this Network Dynamics, Max Planck Inst. Dynamics and limitation, the present study employs the parallel TSQR Self-Org. algorithm of Demmel et al. (2012), which is further used [email protected], [email protected] as a basis of the underlying parallel SVD. This algorithm is shown to scale well on machines with a large number of processors and, therefore, allows the decomposition of very MS55 large data-sets. Compressive Sensing and Dynamic Mode Decom- position Taraneh Sayadi, Peter Schmid Imperial College London This work explores compression and compressive sensing [email protected], [email protected] strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. We demonstrate this architecture on three model systems. MS55 First, we construct a spatial signal from a sparse vector of Using Dynamic Mode Decomposition to Extract Fourier coefficients driven by a linear dynamical system. Linear Global Modes from Nonlinear Fluid Flow Next, we consider the double gyre flow field, which is a Solvers model for chaotic mixing in the ocean. Finally, we explore the 2D cylinder at Re=100. We present a dynamic mode decomposition (DMD) based technique to capture the dominant linear global modes and Steven Brunton eigenvalues using snapshots from a nonlinear flow solver. University of Washington This approach relies on tracking the growth of perturbation [email protected] from the base state with a nonlinear solver. The guidelines for the DMD-based analysis to predict stability properties MS55 of the flow are discussed. Validations are performed against the global stability analysis based on the linearized flow Improving the Accuracy of Dynamic Mode Decom- solver and full eigenvalue problem. position in the Presence of Noise Kunihiko Taira The usefulness of dynamic mode decomposition (DMD) re- Florida State University lies on its ability to extract accurate dynamic features from [email protected] imperfect, noisy data. By deriving the statistical proper- ties of the DMD algorithm, we demonstrate that sensor noise biases the results of DMD in a predictable manner. Aditya Nair We introduce a number of modifications to the DMD algo- Florida State University rithm that give improved robustness to noisy data, which Mechanical Engineering are validated on a range of synthetic, numerical and exper- [email protected] imental data sets. Shervin Bagheri Scott Dawson,MaziarS.Hemati KTH Mechanics DS15 Abstracts 157

Linn´eFlowCentre Robert Vandervorst [email protected] VU Amsterdam Department of Mathematics [email protected] MS56 Morse Homology on Spaces of Braids Marcio Gameiro University of Sao Paulo A Morse Homological theory is constructed on spaces of [email protected] braids, allowing us to consider simultaneously distinct pe- riodic solutions of gradient-like scalar ODEs of the form MS56 − us = utt u + V (t, u, ut) Reconstructing Functions from Dense Samples with possibly different periods simultaneously. This gives Abstract not available. information on existence of certain solutions but also makes it possible to do computation on Floer Homology by linking Vidit Nanda the (very) infinite dimensional Floer Homology and the Department of Mathematics finite dimensional Conley Index of a discretised dynamical University of Pennsylvania system. [email protected] Patrick Hafkenscheid VU University Amsterdam MS57 [email protected] Global Invariant Manifolds Unravelling Shilnikov Chaos MS56 We analyse the role of two-dimensional global invariant Computing Conley-Morse Databases manifolds in the transition through a chaotic Shilnikov Abstract not available. homoclinic bifurcation in a 3D model for an optically in- jected laser. We compute the respective two-dimensional Shaun Harker global manifolds, and their intersection curves with a suit- Department of Mathematics able sphere, as families of orbit segments with a two-point Rutgers University boundary-value-problem setup. This allows us to deter- [email protected] mine how the arrangement of global manifolds changes through the bifurcation and how this influences the topo- logical organisation of phase space. In this way, we find MS56 that the stable manifold of the associated saddle-focus is an Rigorous Computing in Strongly Indefinite Prob- accessible set of the stable manifold of a chaotic saddle (the lems Shilnikov chaotic set) that contains countably many peri- odic orbits of saddle type. In intersection with a suitably Floer homology was originally developed in the late 80s by chosen sphere we find that this stable manifold is an inde- A. Floer to solve the Arnold Conjecture which states that composable continuum consisting of infinitely many closed the number of periodic solutions of a periodic Hamiltonian curves that are locally a Cantor bundle of arcs. system is bounded from below by the topological invari- ants of the manifold on which the Hamiltonian system is Pablo Aguirre defined. In this setting the periodic orbits are the solu- Universidad T´ecnica Federico Santa Mara tions of the Euler-Lagrange equations, i.e. critical points Departamento de Matem´atica of a strongly indefinite action functional. Being an infi- [email protected] nite dimensional version of Morse theory, Floer homology is defined in terms of (1) the critical points; (2) their rela- Bernd Krauskopf, Hinke M. Osinga tive indices; and (3) the connecting orbits between critical University of Auckland points with relative index one. While Floer homology is a Department of Mathematics powerful and celebrated theory, there remains an outstand- [email protected], [email protected] ing issue: how computable is it? Recent years have wit- nessed the development of exciting rigorous computational methods to make Conley-Morse homology computable and MS57 applicable to a broad class of dynamical systems. Now The Lorenz System Near the Loss of the Foliation the question is: can we do the same with Floer-Morse Condition homology? In this talk, we introduce some preliminary results about rigorous computing in Floer homology, i.e. We consider the onset of hooks in the Poincar´ereturnmap we present a rigorous computational technique to compute of the famous Lorenz system, when the one-dimensional critical points of strongly indefinite functional as well as Lorenz map ceases to accurately represent the dynamics. their relative indices. We employ a two-point boundary value problem set-up to calculate a point of tangency of the two-dimensional unsta- Jean-Philippe Lessard ble manifold W u(Γ) of a periodic orbit Γ with the stable Universit´eLaval foliation. This allows us to continue this boundary curve [email protected] in any of the system parameters.

Jan Bouwe Van Den Berg Jennifer L. Creaser VU University Amsterdam University of Auckland [email protected] [email protected] 158 DS15 Abstracts

Bernd Krauskopf, Hinke M. Osinga a permanent shift of their parameters. We illustrate via University of Auckland a conceptual climate model that this nonergodic snapshot Department of Mathematics framework might be useful in Earth System dynamics. [email protected], [email protected] Gabor Drotos Eotvos University MS57 [email protected] Analytic Proof of Lorenz Attractors in Flows and Maps Tamas Bodai Meteorologisches Institut In this talk I will give an overview of the recent results re- Universit¨at Hamburg garding the theoretical proof of the birth of strange Lorenz [email protected] attractors in various models. This includes the criteria of the birth of Lorenz attractors from global bifurcations of Tamas Tel flows (double homoclinic loop), which were also applied E¨otv¨os Lor´and University, Budapest, Hungary to prove analytically (without a computer assistance) that Institute for Theoretical Physics such an attractor is present in the Lorenz model (the 14th [email protected] Smale’s problem). This result allows to obtain conditions of the birth of Lorenz attractors in local bifurcations of flows as well as local and global bifurcations of diffeomor- MS58 phisms. Random Attractors and How They Help Under- stand Climate Change and Variability Ivan Ovsyannikov University of Bremen, Germany Until recently, there were two basic approaches to appre- [email protected] hend the complexity of climate change: deterministically nonlinear and stochastically linear, or the Lorenz and the Hasselmann approach. The theory of random dynami- MS57 cal systems provides a framework for unifying these two The Many Facets of Chaos approaches. We apply this theory to study the random attractors of nonlinear, stochastically perturbed climate There are many ways that a person can encounter chaos, models, and define climate sensitivity via Wasserstein dis- such as through a time series from a lab experiment, a tances between such attractors. Numerical results are pre- basin of attraction with fractal boundaries, a map with a sented for a highly simplified ENSO model. crossing of stable and unstable manifolds, a fractal attrac- tor, or in a system for which uncertainty doubles after some Michael Ghil time period. These encounters appear so diverse, but the Ecole Normale Sup´erieure, Paris, and chaos is the same in all of the underlying systems; it is University of California, Los Angeles just observed in different ways. We describe these differ- [email protected] ent types of chaos. We will give two conjectures about the types of dynamical behavior that is observable if one ran- domly picks out a dynamical system without searching for MS58 a specific property. In particular, we conjecture that from Snapshot Attractors and the Transition to Exten- picking a system at random, one observes (1) only three sive Chaos in Large Systems of Mean-Field Cou- types of basic invariant sets: periodic orbits, quasiperiodic pled Oscillators orbits, and chaotic sets; and (2) that all the definitions of chaos are in agreement. We consider systems of many (N) mean-field coupled oscil- lators with two types of dynamics: low dimensional attrac- Evelyn Sander tors (in which the oscillator states all clump into just a few George Mason University values), and extensively chaotic states (in which the attrac- [email protected] tor dimension scales linearly with N). We use the concept of snapshot attractors to analyze extensively chaotic states focusing on the associated fractal dimension. We also study MS58 dynamical transitions from low dimensional attractors to The Quantification of the Nonergodic Property Via extensive chaos and vice verse. Snapshot Attractors: An Application to a Concep- Edward Ott tual Climate Model University of Maryland The natural measure of a snapshot attractor can be approx- Inst. for Research in Electronics and Applied Physics imated only with the use of an ensemble of trajectories. We [email protected] quantitatively describe the limitations for extracting esti- mates on the relevant probabilities from the time evolu- Wai Lim Ku tion of a single trajectory. For instance, temporal averages Univ. of Maryland over finite time intervals taken along a single trajectory are [email protected] found to typically differ from the corresponding ensemble averages. This can be regarded as a measure of the non- Michelle Girvan ergodic property. In addition, we introduce further, prob- University of Maryland abilistic measures for nonergodicity. We show that even [email protected] in stationary systems ergodic behavior sets in for asym- totically long times, no characteristic time exists for the convergence. Ergodicity is typically broken down even for MS58 asymtotically long times in nonautonomous systems with SRB Measures for Time-Dependent and Random DS15 Abstracts 159

Attractors Celso Bernardo Freitas Instituto Nacional de Pesquisas Espaciais - INPE For autonomous systems of ODEs with chaotic attractors, Sao Jose dos Campos, SP, Brasil large-time orbit distributions are described by SRB mea- [email protected] sures. This theory carries over very well to random dynam- ical systems, for which the picture is in fact simpler due to Ricardo L. Viana the averaging effects of random noise. Some of the ideas Departmento de Fisica extend even to time-dependent attractors without any no- Federal University of Parana tion of stationary. I will review known ideas and report on viana@fisica.ufpr.br new results.

Lai-Sang Young MS59 Courant Institute of Mathematical Sciences Chimera States in Networks with Symmetry- New York Univ. Breaking Coupling [email protected] In a network of Stuart-Landau oscillators with nonlocal topology and symmetry-breaking coupling we establish MS59 novel partially coherent inhomogeneous spatial patterns, Chimeras in Networks of Identically Coupled Me- which combine the features of chimera states (coexisting chanical Oscillators incongruous coherent and incoherent domains) and oscilla- tion death (oscillation suppression), which we call chimera Synchronization has been vastly observed in nature as well death. Moreover, we find chimera states with respect as in man-made systems. Synchronous states are possi- to amplitude dynamics rather than the phase (amplitude ble when two or more oscillators are interacting with each chimeras). Additionally, we show that two distinct scenar- other. In particular, arrays of identical oscillators can ex- ios from oscillatory behavior to a stationary state regime hibit a fascinating spatiotemporal pattern, termed chimera are possible: a transition from an amplitude chimera to state, in which synchronous domains coexist with inco- chimera death via in-phase synchronized oscillations, and herent ones. Previous studies have addressed this phe- a direct abrupt transition for larger coupling strength. We nomenon theoretically and experimentally. However, the believe our results are of particular importance for the life spontaneous emergence of chimeras in translationally in- sciences. For instance, these peculiar hybrid states may variant networks remains an experimental challenge. Here, account for the observation of partial synchrony in neural we use a one-dimensional network of identically coupled activity, like unihemispheric sleep etc. A. Zakharova, M. identical mechanical oscillators, to implement an experi- Kapeller, E. Sch¨oll, Chimera Death: Symmetry Breaking mental demonstration yielding this unique phenomenon. in Dynamical Networks, Phys. Rev. Lett. 112, 154101 Our findings, supported by a mathematical model, bring (2014) new insights into the search for chimeras in nature. Anna Zakharova Rosangela Follmann Institute of Theoretical Physics Polytechnic School of University of Sao Paulo Berlin, Germany [email protected] [email protected]

Daniel Abrams, Adilson E. Motter Marie Kapeller Northwestern University Berlin Institute of Technology [email protected], [email protected] Berlin, Gernamy [email protected]

MS59 Eckehard Sch¨oll Synchronization Properties Related to Neighbor- Technische Universit¨at Berlin hood Similarity in a Complex Network of Non- Institut f¨ur Theoretische Physik Identical Oscillators [email protected]

We explore in this article complex networks of non-identical interacting oscillators. More specif- ically, the impact of MS59 Similar or Dissimilar neighborhoods over the emergence Dynamics of Clustering in Networks with Repul- of synchronization is studied. These scenarios are defined sive Interaction based on a vertex weighted graph measure, the Total Disso- nance, which comprises the sum of the dissonances between In dynamics of simple coupled systems attracting interac- all neighbor oscillators in the network. Our numerical sim- tion usually leads to synchronization. In contrast, repulsive ulations show that the more homogeneous is a network, interaction is able to split the ensemble into clusters, to the higher tend to be both the coupling strength required create multistability and, as we will show, in certain cases to phase-lock and the associated final phase configuration even generate continuous families of oscillatory states. spread over the circle. On the other hand, the initial spread of partial synchronization occurs faster for Similar neigh- MichaelA.Zaks borhoods in comparison to Dissimilar ones. Department of Stochastic Processes, Institute of Physics Humboldt University of Berlin Elbert E. Macau [email protected] INPE - Brazilian National Institute for Space Research LAC - Laboratory for Computing and Applied Mathematics MS60 [email protected] Dynamic Mode Decomposition for Multi- 160 DS15 Abstracts

Resolution Analysis gorithms and Applications

The dynamic mode decomposition (DMD) is an ideal We present two extensions of Extended Dynamic Mode De- method for decomposing complex systems into spatio- composition (EDMD), which is a data-driven method that temporal modes with prescribed temporal signatures. The approximates the eigenvalues, eigenfunctions, and modes frequency and duration of the data collection process can of the Koopman operator. The first is algorithmic: we be adapted, much as in wavelet theory, to sift out infor- show that EDMD can be rewritten as a kernel method, mation at different temporal scales. Indeed, an iterative which enables Koopman-based computation in large sys- refinement of progressively shorter snapshot sampling win- tems to be performed. The second is an application: the dows and recursive extraction of DMD modes from slow- Koopman eigenfunctions are used as a set of intrinsic coor- to increasingly-fast time scales allows for a multi-resolution dinates that enable data-fusion/state-reconstruction tasks DMD analysis that allows for improved analytics. More- to be accomplished. over, it also allows for improved analytic predictions of the short-time future state of the system which is of critical Matthew O. Williams importance for control protocols. Program in Applied and Computational Mathematics Princeton University J. Nathan Kutz [email protected] University of Washington Dept of Applied Mathematics MS61 [email protected] What Is the Right Functional for Variational Data Assimilation? MS60 Variational data assimilation refers to matching model tra- Approximating the Koopman Operator Using Ex- jectories with observations. This is usually accomplished tended Dynamic Mode Decomposition by minimising a quadratic error functional which, in dis- crete time with gaussian perturbations, can be interpreted It has recently been observed that eigenvalues and modes as the likelihood of a trajectory. Different ways to solve of the Koopman operator may be approximated using a this problem though can lead to different solutions in the data-driven algorithm called Dynamic Mode Decomposi- limit of Δt → 0. This corresponds to the fact that in con- tion (DMD). We first provide a new definition of DMD that tinuous time, there are several contenders for the likelihood is equivalent to the original, but is more amenable to anal- of a trajectory. ysis. We then describe an Extended DMD method which approximates the Koopman operator directly, using a user- Jochen Br¨ocker specified set of basis functions, and allows one to compute University of Reading, UK Koopman eigenvalues, modes, and eigenfunctions. School of Mathematical and Physical Sciences [email protected] Clarence Rowley Princeton University Department of Mechanical and Aerospace Engineering MS61 [email protected] Time Delay Methods for Variational Data Assimi- lation Matthew O. Williams Program in Applied and Computational Mathematics We investigate an extension to variational data assimilation Princeton University by modifying the minimized cost function. A penalty to the [email protected] cost function is added if the state vector at a given time is inconsistent with the measurements at a later time. The idea is to inform the choice of unmeasured state variables MS60 by looking at how they affect the observed dynamics over a window of time, rather than comparing the optimum path Koopman Operator Techniques in Power Grid only at adjacent times. Analysis Uriel I. Morone Spectral properties of the so-called Koopman operator pro- UCSD vide an alternative framework for dynamical systems anal- [email protected] ysis. This enables a new technique of nonlinear modal de- composition, which is referred to as the Koopman Mode Decomposition (KMD). In this presentation, we will out- MS61 line our recent efforts on applications of KMD to analysis of Filtering Unstable Quadratic Dissipative Systems power grid dynamic performances such as stability analysis and network partitioning. This will lead to a data-driven The long-time behavior of filters for partially observed framework of analysis and operation of the future power quadratic dissipative dynamical systems is considered. It is grid that can handle high penetration of renewable energy proven that for both discrete-time and continuous-time ob- resources. servations the 3DVAR filter can recover the signal within a neighborhood defined by the size of the observational noise, Yoshihiko Susuki as long as a sufficiently large proportion of the state vec- Kyoto University / JST-CREST tor is observed; an explicit form for a sufficient constant [email protected] observation operator is given. Three models of interest fit into this class – Lorenz ’63, Lorenz ’96, and 2D Navier- Stokes on a torus. Furthermore, in the case of Lorenz MS60 ’96, non-constant adaptive observation operators are stud- Machine Learning and the Koopman Operator: Al- ied numerically, with data incorporated by use of both the DS15 Abstracts 161

3DVAR and the extended Kalman filter. It is shown that University of Washington for carefully chosen adaptive observations, the proportion [email protected] of state coordinates necessary to accurately track the sig- nal is significantly smaller than the proportion proved to Raissa D’Souza be sufficient for constant observation operator. Indeed it is UC Davis shown that the necessary number of observations may even [email protected] be significantly smaller than the total number of positive Lyapunov exponents of the underlying system. MS62 Kody Law SRI UQ Center, CEMSE, KAUST Intrinsic Computation in NEMS [email protected] The ways in which nanoscale systems generate, store, and Abhishek Shukla process information and dissipate energy yield insights into Warwick their behavior, potential technological functions, and fun- [email protected] damental physics of computation. Nanoelectromechanical systems (NEMS) are nonlinear and subject to thermal fluc- Daniel Sanz-Alonso tuations, making them an ideal experimental platform to University of Warwick probe the trade-offs between intrinsic computation and en- [email protected] ergy use. I will present results quantifying intrinsic com- putation in the dynamics of the theoretical counterpart of many NEMS devices, the noisy Duffing oscillator. Andrew Stuart Mathematics Institute, Russell Hawkins University of Warwick UC Davis [email protected] Complexity Sciences Center [email protected] MS61 Observability of Chaotic Lorenz-96 Systems MS62 In 1996 E. Lorenz proposed a ring of one-dimensional Phase Synchronization Between Nanoelectrome- ODEs for describing some meteorological quantity at chanical Oscillators equidistant locations along a latitude circle. Since then this systems became a frequently used hyperchaotic model Synchronization, the mutual entrainment of limit cycle os- for exploring new concepts in dynamical systems theory. cillators, is a ubiquitous phenomenon both in the physical In our contribution we shall use it as a prototypical ex- and biological sciences. There exist many observation stud- ample for illustrating, testing, and comparing methods for ies of this phenomenon; however, controlled experiments in observability analysis, and state and parameter estimation. this field are scant. In this talk, I will describe an experi- ment in synchronization based on NanoElectroMechanical (NEMS) oscillators. In addition to the ability to measure Jan Schumann-Bischoff the amplitude and phase dynamics of individual nodes, the Max Planck Institute for Dynamics and Self-Organization experiment demonstrates a large degree of control over the jan.schumann-bischoff@ds.mpg.de parameters of the system. Both the coherent and stochas- tic dynamics will be discussed. Stefan Luther, Ulrich Parlitz Max Planck Institute for Dynamics and Self-Organization Matt Matheny Research Group Biomedical Physics California Institute of Technology [email protected], [email protected] [email protected]

MS62 MS63 Control of Complex Diffusion in Networks of NEMS Ensemble Inflation by Shadowing Techniques

Recent advances in NEMS enable us to explore nonlinear The artificial inflation of ensembles is a technique com- phenomena on networks in unprecedented ways. We apply mon to ensemble data assimilation whereby the ensemble methods from control of complex diffusion to the oscilla- variance is increased in order to prevent deviation of the tors’ complex envelopes as coupled via a linear diffusion ensemble from the truth. Various techniques for inflating term. We focus on network synchronization and our ability ensembles exist in the literature. This talk will discuss to guide the system to synchronized states by controlling ensemble shadowing and our implementation of shadow- a small number of oscillators’ natural linear frequencies. ing techniques as a method of ensemble inflation. We will Additionally, we investigate control of other limit cycles in also present results from a low order chaotic system that small systems with simple network structure. support using shadowing inflation.

Jeff Emenheiser Thomas Bellsky UC Davis Arizona State University Physics Department [email protected] [email protected] Lewis Mitchell Mehran Mesbahi University of Adelaide 162 DS15 Abstracts

[email protected] [email protected]

Irina Rypina MS63 Woods Hole Oceanographic Institution Ionospheric Weather Forecasting Using the Letkf [email protected] Scheme

We assimilate satellite observations to forecast ionospheric MS64 electron density using the Local Ensemble Transform A Mechanism of Spiral Wave Unpinning and Its Kalman Filter(LETKF). This assimilation scheme gener- Implications for the Treatment of Cardiac Arrhyth- ates forecasts from an ensemble of initial conditions and mias with Periodic Far-Field Pacing forms its analysis by computing a unique linear combi- nation of the forecast ensembles at each grid point using Spiral waves pinned to inexcitable regions of tissue pose nearby observations. The ionosphere model used is the a particular challenge in the effort to control cardiac ar- TIEGCM. Assessments of the LETKF include validation rhythmias without a strong defibrillating electrical shock. against independent data sources as well as skill in esti- We investigate one particular unpinning mechanism due mating ionospheric drivers, forecast ensemble uncertainty, to far-field pulses in a two-dimensional model of excitable and spatially sharp electron density gradients. media and determine its potential benefits over alternative low-energy strategies such as anti-tachycardia pacing. Fur- Juan Durazo thermore, we explore how a simple map-based model can Arizona State University predict success rates for more realistic scenarios involving [email protected] periodic stimuli. Philip Bittihn MS63 Biodynamics Lab Predicting Flow Reversals in a Cfd Simulated Ther- University of California, Sandiego mosyphon Using Data Assimilation [email protected]

A thermal convection loop is a circular chamber filled with Anna Behrend water, heated on the bottom half and cooled on the top Max Planck Institute for Dynamics and Self-Organization half. With sufficiently large forcing of heat, the direction G¨ottingen, Germany of fluid flow in the loop oscillates chaotically, forming an [email protected] analog to the Earths weather. As is the case for state-of- the-art weather models, we only observe the statistics over Stefan Luther a small region of state space, making prediction difficult. Max Planck Institute for Dynamics and Self-Organization To overcome this challenge, data as- similation methods, Research Group Biomedical Physics and specifically ensemble methods, use the computational [email protected] model itself to estimate the uncertainty of the model to optimally combine these observations into an initial con- dition for predicting the future state. First, we build and MS64 verify four distinct DA methods. Then, a computational The Effects of Cardiac Fibroblasts on Wave Propa- fluid dynamics simulation of the loop and a reduced order gation in Ventricular Tissue: Insights from Numer- model are both used by these DA methods to predict flow ical Studies of Mathematical Models reversals. The results contribute to a testbed for algorithm development. We study spiral-wave turbulence in partial-differential- equation models for human cardiac tissue, with both my- Andrew Reagan ocytes and fibroblasts. We obtain results for cells, with one University of Vermont myocyte coupled to several fibroblasts, and for tissue. We [email protected] study (a) regularly and (b) randomly arranged fibroblasts, systematize their role in modifying the cardiac action po- tential and the propagation of activation waves, and inves- MS63 tigate a low-amplitude control scheme for the suppression An Application of Lagrangian Data Assimilation to of spiral-wave turbulence. Katama Bay, Ma Alok R. Nayak Lagrangian data assimilation (LaDA) methods directly use Indian Institute of Science, Bangalore, India observations of passive drifters in a flow in order to estimate [email protected] the underlying currents. We apply the ensemble Kalman filter in this context to a model of Katama Bay in Martha’s Rahul Pandit Vineyard, using real drifter observations. We compare the Indian Institute of Science, Bangalore augmented-vector method of LaDA to so-called pseudo- [email protected] Lagrangian methods. Finally, we judge the method‘s per- formance using Eulerian data of the bay from the same time. MS64 How to Control Spiral Waves Using Weak Signals: Laura Slivinski A Few Suggestions Woods Hole Oceanographic Institution [email protected] In this talk I will describe a few recently developed meth- ods to control dynamics of spiral waves and spatiotemporal Larry Pratt chaos in excitable media. Control is achieved by the ap- Woods Hole Oceanographic Inst. plication of small amplitude external signals in a fashion DS15 Abstracts 163

designed to exploit nonlinear properties of excitable sys- Gunnar Seemann tems. Payoffs for the experimental realisation of such ro- Karlsruhe Institute of Technology bust methods to control spiral dynamics is enormous and Germany could have several practical applications, potentially in- [email protected] cluding a device for safe cardiac defibrillation. Henggui Zhang S Sridhar University of Manchester Ghent University, Belgium UK [email protected] [email protected]

MS64 MS65 Controlling Spiral Wave Dynamics in Cardiac Stabilized Wave Segments in An Excitable Medium Monolayers Using Far Field Pulses with a Phase Wave at the Wave Back

Waves in two-dimensional excitable media forms patterns We determine analytically the propagation velocity and the such as target waves and spiral waves. Spiral waves tend to shape of stationary propagating wave segments in excitable attach to the heterogeneities in the medium and form very media supporting excitation waves with trigger fronts and stable structures. We study controlling such waves using phase backs. Relationship between the medium excitabil- far field electric pulses in two-dimensional layers of cultured ity and the wave segment parameters is described using cardiac cells. We will discuss resetting and terminating the free boundary approach. This leads to two univer- spiral waves using periodic far field pulses. sal limits, restricting the region of existence of stabilized wave segments. Comparison of the analytical results with Shajahan Thamara Kunnathu numerical simulations of the Kessler-Levine model demon- Max Planck Institute for Dynamics and Self Organization strates their good quantitative agreement. [email protected] Eberhard Bodenschatz Sebastian Berg Max Planck Institute for Dynamics & Self-Organization Max Planck Institute for Dynamics and Self-Organization [email protected] Research Group Biomedical Physics [email protected] Vladimir Zykov Max Planck Institute for Dynamics and Self-Organization Valentin Krinsky [email protected] Max Planck Institute for Dynamics and Self-Organization [email protected] MS65 Stefan Luther Use of Delay-Differential Equations in Cardiac Max Planck Institute for Dynamics and Self-Organization Models Research Group Biomedical Physics [email protected] Period-2 behavior of cardiac electrical responses, referred to as alternans, often leads to more complicated arrhyth- mias. To date, alternans has been generated mathemati- MS65 cally from the loss of stability of the period-1 solution in coupled nonlinear ODE/PDE systems. We build on the Anatomy Induced Drift of Reentrant Waves in Hu- fact that delays arise naturally in non-instantaneous cel- man Atrium lular processes and present an alternative approach using delay-differential equations (DDEs), which are known to In biophysically and anatomically realistic model of human promote complex dynamics. We analyze the dynamical atrium, we demonstrate functional effects of atrial anatom- behaviors of our DDE system and discuss the implications ical structures on reentrant waves spontaneous drift. Spiral of our findings. waves drift from thicker to thinner regions, along ridge-like structures of pectinate muscules (PM) and cristae termi- Elizabeth M. Cherry,RyanThompson nalis, anchor to PM-atrial wall junctions or to some loca- Rochester Institute of Technology tions with no obvious anatomical features. The insight can School of Mathematical Sciences be used to improve low-voltage defibrillation protocols, and [email protected], [email protected] predict atrial arrhythmia evolution given a patient specific atrial anatomy. MS65 Irina Biktasheva Spiral Wave Activity in a Mixture of Resting University of Liverpool and Oscillating Cardiomyocytes: Limitations on [email protected] Biopacemaker Development

Vadim N. Biktashev Self-organization of interconnected elements is important College of Engineering, Mathematics and Physical for development of biopacemakers. Monolayers of pluripo- Sciences tent cell-derived cardiomyocytes exhibit spontaneous acti- University of Exeter vation and consist of a heterogeneous network of cells. A [email protected] simple stochastic model of cell distributions combined with a Fitzhugh-Nagumo type model highlights the importance Sanjay R. Kharche of spatial granularity of spontaneous cells on biopacemaker University of Exeter activity. Interestingly, spiral wave activity and the desired [email protected] simultaneous activation of the biopacemaker are found in 164 DS15 Abstracts

opposite spectrum of oscillating cell spatial patterns. [email protected]

Philippe Comtois Institute of Biomedical Engineering, MS66 Universite de Montreal Finite Size Effects in Networks of Theta Neurons [email protected] The dynamics of a large but finite number of coupled spik- ing neurons is not well understood. We analyze finite size MS66 effects in a network of synaptically coupled theta neurons. We show how the system can be characterized by a func- Traveling Waves in a Laminar Neural Field Model tional integral from which finite size effects are calculated of Visual Cortex perturbatively. We consider how finite size effects affect the stability of the asynchronous state of a uniformly cou- One of the challenges in the mathematical and computa- pled network. We then discuss the implications for bump tional modeling of primary visual cortex (V1) is develop- attractors. ing recurrent networks models that keep track of neural activity with respect to both retinotopic and feature-based Siwei Qiu degrees of freedom such as orientation selectivity. This is NIDDK/LBM further complicated by the fact that different cortical layers NIH have different response properties. In this talk we present a [email protected] laminar neural field model consisting of a superficial layer of orientation-selective cells interacting vertically with a Carson C. Chow deep layer of non-orientation selective cells. We use the National Institutes of Health model to analyze the propagation of orientation selectivity [email protected] across cortex.

Samuel R. Carroll MS66 University of Utah Optimal Decision-Making in a Changing Environ- [email protected] ment

Paul C. Bressloff We derive a continuous stochastic differential equation de- University of Utah scribing the optimal accumulation of evidence in a chang- Department of Mathematics ing environment. Our results apply to two choice decision bressloff@math.utah.edu making wherein the underlying truth switches stochasti- cally. Sequential analysis is used to determine the prior probabilities of finding the truth in one of two states. Pass- MS66 ing to the continuum limit and non-dimensionalizing, we find the evidence accumulation process depends on a single A Computational Model of the Influence of Depo- parameter, information received per mean switch time. larization Block on Initiation of Seizure-like Activ- ity Alan Veliz-Cuba University of Houston Seizure-like activity can be triggered in a network of ex- Rice University citatory and inhibitory neurons when excessive excitation [email protected] is not suppressed by matching inhibition. Recent exper- imental studies report that inhibitory neurons, receiving Zachary Kilpatrick strong excitatory drive, were functionally impaired due University of Houston to depolarization block prior to propagation of ictal dis- [email protected] charges. In this talk, we will discuss different types of dynamics emerging from a network of excitatory and in- Kreimir Josic hibitory neurons when inhibitory neurons are prone to de- Department of Mathematics, University of Houston polarization block. We find that the network may reach [email protected] the pathological state via saddle-node bifurcation or ho- moclinic bifurcation. Oscillatory activity present in the network allows us to produce tonic to clonic phase transi- MS67 tion observed in epileptic brain slices and human patients. Costs and Benefits of Mutational Robustness in We also discuss the effects of network motifs on promot- Rna Viruses ing pathological dynamics. The convergent motifs from excitatory neurons onto inhibitory neurons, which may be The accumulation of mutations in RNA viruses is thought observed in mossy fiber sprouting, facilitates depolariza- to facilitate rapid adaptation to changes in the environ- tion block in inhibitory neurons so that the network can ment. However, most mutations have deleterious effects, enter the pathological state more easily. The mean field especially for viruses. Thus, tolerance to mutations should equation accounting for the network structure allows us to determine the nature and extent of genetic diversity in the make predictions about the effects of different type of net- population. I will present a combination of population ge- work motifs. The predictions from the mean field model netics theory, computer simulation, and experimental evo- are verified by simulating a network of conductance-based lution to examine the advantages and disadvantages of tol- neurons. erance to mutations, also known as mutational robustness.

Duane Nykamp School of Mathematics Simone Bianco University of Minnesota IBM Research DS15 Abstracts 165

[email protected] [email protected]

MS67 MS67 Thermodynamics and Statistical Mechanics of Vi- Evolutionary Dynamics of Mutator Phenotypes in ral Evolution Changing Environments We analyze a simplified model of viral infection and evo- lution using the grand canonical ensemble and formalisms Stochastic switching is an example of phenotypic bet- from statistical mechanics and thermodynamics to calcu- hedging, where offspring can express a phenotype different late the behavior of a macroscopic number of viruses, and from that of their parents. Even though phenotypic switch- to derive thermodynamic variables for the system. We ing is well documented in viruses, yeast, and bacteria, there model the infection process as a series of energy barriers has been little exploration of the evolution of these muta- determined by the genetic states of the virus and host as tor phenotypes under spatially and temporally fluctuating a function of immune response and system temperature. selection pressures. In this talk, I will use a population We find a phase transition between a positive temperature genetic model to explore the interaction of temporal and regime of normal replication and a negative temperature spatial variation in determining the evolutionary dynam- disordered phase of the virus. These phases define differ- ics of phenotypic switching. Although the formulation of ent regimes in which different genetic strategies are favored. the model is in terms of non-genetic switching, the same Perhaps most importantly, it demonstrates that the sys- framework can be used to study the evolution of genetic tem has a real thermodynamic temperature. For normal mutation rates under volatility in selection. This study replication, this temperature is linearly related to effective offers new insights into how the interplay of spatial and temperature. For all temperatures and immunities studied, temporal environmental variability can influence the evo- we find a universal curve relating the order parameter to lution of phenotypic switching rates, mutation rates, or viral evolvability. Real viruses have finite length RNA seg- other sources of phenotypic variation. ments that encode for proteins which determine their fit- ness; hence the methods put forth here could be refined to Oana Carja apply to real biological systems; perhaps providing insight University of Pennsylvania into immune escape, the emergence of novel pathogens and [email protected] other results of viral evolution. Barbara Jones,JamesKaufman IBM Research MS67 [email protected], [email protected] The Acceleration of Evolutionary Spread by Long- Range Dispersal Justin Lessler Johns Hopkins Bloomberg School of Public Health [email protected] The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spread- MS68 ing dynamics not only depends on fitness differences but Characterizing the Structure of Multilayer Net- also on the dispersal be- havior of the species. Spreading works at a constant speed is gener- ally predicted when disper- sal is sufficiently short-ranged, specifically when the dis- The development of Complex Network’s Theory is provid- persal kernel falls-off exponentially or faster. However, ing radical new ways of understanding many different pro- the case of long-range dispersal is unresolved: While it is cesses from physical, social, engineering, information and clear that even rare long-range jumps can lead to a dras- biological sciences. Several notions, such as networks of tic speedup as air-trafficmediated epidemics show it has networks, multidimensional networks, multilevel networks, been difficult to quantify the ensuing stochastic dynami- multiplex networks, interacting networks, interdependent cal pro- cess. Yet, such knowledge is indispensable for a networks, and many others have been introduced, and even predictive understanding of many spreading processes in different mathematical approaches, based on tensor repre- natural populations. I present a simple iterative scaling sentation have been proposed. In this talk we will discuss approximation supported by simulations that accurately a general framework for multilayer networks that includes predicts evo- lutionary spread which is determined by a the great majority of the different approaches addressed so tradeoff between frequency and potential effectiveness of far in the literature and review some of attempts to ex- long-distance jumps. In contrast to the exponential laws tend the notions, measures and models from single layer to predicted by deterministic mean- field approximations, we multilayer networks. show that the asymptotic spatial growth is either according to a power-law or a stretched exponential, depending on the Regino Criado tails of the dispersal kernel. More importantly, we provide Universidad Rey Juan Carlos a full time-dependent description of the convergence to the [email protected] asymptotic behavior which can be anomalously slow and is relevant even for long times. I will discuss to what extend Miguel Romance our results might be used to improve the inference of the Departamento de Matematica Aplicada evolutionary spread based on genealogical trees, which is Universidad Rey Juan Carlos however a largely open problem. [email protected]

Oskar Hallatschek Department of Physics MS68 UC Berkeley Synchronization and the problem of Targeting in 166 DS15 Abstracts

Multilayer Networks state when the network topology evolution is fully general, and not necessarily restricted to commuting structures. We concentrate on the case involving a two-layer master- slave network to steer a desired collective behavior, not nec- Charo I. del Genio essarily synchronous. The problem is here tackled through University of Warwick a Master Stability Function approach, assessing the stabil- [email protected] ity of the aimed dynamics, and through a selection of nodes to be targeted. We show that the degree of a node is a cru- cial element in this selection process, and that the target- MS69 ing mechanism is most effective in heterogeneous scale-free The Response of Statistical Averages to Small architectures. Stochastic Forcing

Ricardo Gutierrez We present a response theory for statistical averages of Department of Chemical Physics deterministic dynamical systems perturbed by a small The Weizmann Institute of Science stochastic forcing. We derive the response formula ex- [email protected] plicitly in terms long-time averages of the tangent map of the unperturbed system, and show that the response Irene Sendina Nadal is the second-order effect with respect to the magnitude Universidad Rey Juan Carlos of perturbation. We also demonstrate that for a finite re- [email protected] sponse time the response is consistent with the prediction of the classical response theory for stochastic systems with smooth invariant distribution density perturbed by a small Massimiliano Zanin stochastic forcing. Technical University of Madrid [email protected] Rafail Abramov Department of Mathematics, Statistics and Computer David Papo Science Universidad Polit´ecnica de Madrid, Spain University of Illinois at Chicago [email protected] [email protected]

Stefano Boccaletti CNR-Istituto dei Sistemi Complessi MS69 [email protected] Is Our Sensing Compressed? Considering many natural stimuli are sparse, can a sensory MS68 system evolve to take advantage of sparsity? We show sig- nificant downstream reductions in the numbers of neurons Game and Diffusion Dynamics in Multilayer Net- transmitting stimuli in early sensory pathways might be a works consequence of sparsity. Our work points to a potential Besides the structure of interactions within networks, also mechanism for transmitting stimuli related to compressed- the interactions between networks are of the outmost im- sensing (CS) data acquisition. Through simulation, we ex- portance. We therefore study the outcome of the evolution- amine the characteristics of networks that optimally en- ary games on multilayer networks that are connected by code sparsity and the role of receptive fields in stimulus means of a utility function, which determines how payoffs sampling. on networks jointly influence the success of players in each Gregor Kovacic individual network.. To reach this aim, we consider the Rensselaer Polytechnic Inst symmetric, asymmetric utility function and find the sym- Dept of Mathematical Sciences metric breaking phenomenon and the spontaneous emer- [email protected] gence of multilayer network reciprocity. Along this line, the role of partially correlation is investigated and the optimal condition for cooperation is found. Finally, we consider the MS69 co-evolution mechanisms of evolutionary games on multi- A Multiscale Method for Optical Responses of layer networks and find that the optimal cooperation can Nano Structures be attributed to individual self-organization trait. We introduce a new framework for the multiphysical Zhen Wang modeling and multiscale compu- tation of nano-optical Baptist University of Hong Kong responses. The semi-classical theory treats the evolu- [email protected] tion of the electromagnetic field and the motion of the charged particles self-consistently by coupling Maxwell equations with Quantum Mechanics. To overcome the nu- MS68 merical challenge of solving high dimensional many body Synchronization in Time Varying Networks: the Schr¨odinger equations involved, we adopt the Time Depen- Non Commutative Case dent Current Density Functional Theory (TD-CDFT). In the regime of linear responses, this leads to a linear sys- We provide a rigorous solution to the problem of construct- tem of equations determining the electromagnetic field as ing a structural evolution for a network of identical cou- well as current and electron densities simultaneously. A pled dynamical units switching between topologies without self-consistent multiscale method is proposed to deal with structural constraints. Our method guarantees that the the well separated space scales. Numerical examples are coupling matrices eigenvectors change smoothly in time. presented to illustrate the resonant condition. This allows to extend the Master Stability Function formal- ism, and to use it to assess the stability of a synchronized Di Liu DS15 Abstracts 167

Michigan State University Division of Applied Mathematics Department of Mathematics Brown University [email protected] bjorn [email protected]

MS69 MS70 Parareal Methods for Highly Oscillatory Dynami- Slow-Fast Factorization of the Evans Function Via cal Systems the Riccati Transformation in the Semi-Strong Regime We introduce a multiscale parareal method that efficiently numerically integrates highly oscillatory ordinary differen- The complexity of singularly perturbed linear stability tial equations. The algorithm computes a low-cost approx- problems can be reduced by factorizing the Evans function imation of all slow variables in the system. Then, fast in accordance with the scale separation. The factoriza- phase-like variables are ob- tained using the parareal it- tion has always been established by geometric arguments, erative methodology and an alignment algorithm. The customized for the specific equations and solutions under method may be used either to enhance the accuracy and consideration. We present an alternative method, that for- range of applicability of the multiscale method in approx- malizes and generalizes the factorization procedure. This imating only the slow variables, or to resolve all the state analytic method is based on the Riccati transformation. variables. The numerical scheme does not require that the We employ our techniques to study the spectral stability system is split into slow and fast coordinates. Moreover, of semi-localized periodic pulse patterns. the dynamics may involve hidden slow variables, for exam- ple, due to resonances. Convergence of the parareal itera- Bj¨orn De Rijk tions is proved and demonstrated in numerical examples. Leiden University [email protected] Richard Tsai Department of Mathematics Arjen Doelman University of Texas, Houston Mathematisch Instituut [email protected] [email protected]

MS70 Jens Rademacher University of Bremen Invariant Manifolds of Multi Interior Spike States [email protected] for the Cahn-Hilliard Equation

We construct invariant manifolds of interior multi-spike states for the nonlinear Cahn-Hilliard equation and then MS70 investigate the dynamics on it. An equation for the mo- Travelling Waves for Fully Discretized Bistable tion of the spikes is derived. It turns out that the dy- Reaction-Diffusion Problems namics of interior spikes has a global character and each spike interacts with all the others and with the boundary. We study various temporal and spatial discretization meth- Moreover, we show that the speed of the interior spikes ods for bistable reaction-diffusion problems. The main fo- is super slow, which indicates the long time existence of cus is on the functional differential operators that arise af- dynamical multi-spike solutions in both positive and neg- ter linearizing around travelling waves in the spatially dis- ative time. This result is obtained through the application crete problem and studying how the subsequent discretiza- of a companion abstract result concerning the existence of tion of time affects the spectral properties of these opera- truly invariant manifolds with boundary when one has only tors. This represents a highly singular perturbation that approximately invariant manifolds. we attempt to understand via a weak-limit method based on the pioneering work of Bates, Chen and Chmaj (2003). Peter W. Bates Once this perturbation is understood, one can study the Michigan State University existence and (non)-uniqueness of waves in the fully dis- Department of Mathematics cretized reaction-diffusion system. [email protected] Hermen Jan Hupkes University of Leiden MS70 Mathematical Institute Oscillatory Pulses in FitzHugh-Nagumo [email protected]

It is well known that the FitzHugh-Nagumo system ex- hibits stable, spatially monotone traveling pulses. Also, MS71 there is numerical evidence for the existence of spatially Nonlocal Aggregation Models: A Primer of Swarm oscillatory pulses, which would allow for the construction Equilibria of multi-pulses. Here we show the existence of oscillatory pulses rigorously, using geometric blow-up techniques and Biological aggregations (swarms) exhibit morphologies gov- singular perturbation theory. erned by social interactions and responses to environment. Starting from a particle model we derive a nonlocal PDE Paul A. Carter describing evolving population density. We study equilib- Department of Mathematics ria and their stability via the calculus of variations which Brown University yields analytical solutions. These solutions include features [email protected] such as spatial localization with compact support, mass concentrations, and discontinuous density jumps that are Bjorn Sandstede also observed numerically. We apply our methods to a 168 DS15 Abstracts

model of locust swarms. [email protected]

Andrew J. Bernoff Harvey Mudd College MS71 Department of Mathematics Aggregate Behaviors of Heterogeneous, Delay- [email protected] Coupled Agents

Chad M. Topaz Emerging collective motions of swarms of interacting Macalester College agents are a subject of great interest with a wide range of [email protected] applications. We show, using mean-field analysis, how col- lective motion patterns and segregation of populations of agents with different dynamic properties emerge naturally in a model based on self-propulsion and attractive pair- MS71 wise interactions between delay-coupled agents. We show Fire Ants Build, Morph, and Repair to Survive persistence of behaviors with non-global coupling and re- Floods duced swarm populations, and verify these results through simulation and experiments.

Fire ants are model organisms for studying active self- Klementyna Szwaykowska healing materials. By linking their legs together, they Plasma Physics Divsion build highly interconnected networks that can quickly re- Naval Research Laboratory arrange themselves in response to applied stress. In this [email protected] talk, we present experiments and modeling that elucidate their construction. Spherical rafts of ants morph into pan- Christoffer R. Heckman cakes within minutes; towers are constructed to provide an U.S. Naval Research Laboratory equal compressive load on each ant. We also use plate-on- [email protected] plate rheology to show ants modify their elastic and viscous moduli by rearrangement of their bodies. Particular con- sideration is given to showing how structural shape and Luis Mier-y-Teran material properties arise from movement and interactions Johns Hopkins Bloomberg School of Public Health between ants. [email protected]

David Hu Ira B. Schwartz Georgia Institute of Technology Naval Research Laboratory [email protected] Nonlinear Dynamical Systems Section [email protected]

MS71 MS72 Quantifying Collective Cell Migration During Can- Clustering, Malleability and Synchronization of cer Progression Hodgkin-Huxley-Type Neurons

During cancer progression, tumor cells migrate throughout In this work we consider a ”network of network” of burst- the body, forming clinically dangerous secondary tumors. ing neurons described by the Huber-Braun model. Each This metastatic process begins when cells leave the primary network is coupled internally in a small word scheme while tumor, either as individual cells or collectively migrating each network is coupled to all other networks using the groups. Using quantitative image analysis techniques, we connectivity matrix of the cat cerebral cortex. Three dy- are able to extract motion information from time-lapse im- namical behavior are analyzed: network clustering genera- ages of epithelial sheets with varying malignancy. Adapt- tion, characterized by the coherence of a group of network; ing metrics originally used to study fluid flows we char- malleability of the entire network face small changes in the acterize the dynamics of these cell lines and compare to intra coupling (internal to a network) and inter coupling collective dynamics models. (between networks) parameters; and the synchronization of the entire network. In particular we pay attention in the complex interplay between inter and intra coupling that Rachel Lee makes the network to be very adaptive to small variations Department of Physics on the coupling parameters. University of Maryland College Park [email protected] Sergio R. Lopes, Thiago de L. Prado Department of Physics Haicen Yue Federal University of Parana University of California San Diego lopes@fisica.ufpr.br, [email protected] [email protected] Ricardo L. Viana Wouter-Jan Rappel Departmento de Fisica Department of Physics Federal University of Parana University of California, San Diego viana@fisica.ufpr.br [email protected] Jos´eC.P.Coninck Wolfgang Losert Department of Mathematics Department of Physics Federal Technological University of Parana University of Maryland, College Park [email protected] DS15 Abstracts 169

Juergen Kurths by either (i) only chemical inhibition or by (ii)electrical Humboldt Univ,Germany, Potsdam Institute for Climate coupling first and then chemical inhibition. In both scenar- Impact ios the neuron with the lower firing rate stops spiking for Research, Germany, and Aberdeen University, UK strong enough inhibition, while the faster neuron remains [email protected] active. However, in scenario (ii) the originally slower neu- ron stops spiking earlier, suggesting that synchronization introduces an element of instability into the two-neuron MS72 network. Nontrivial Collective Dynamics in Networks of Pulse Coupled Oscillators Epaminondas Rosa Illinois State University A wealth of complex phenomena arise in coupled phase Department of Physics oscillators – typically associated to various forms of syn- [email protected] chronization – but the collective (macroscopic) dynamics itself is usually regular (either consisting in a fixed point or in a limit cycle for the macroscopic variables). This MS73 is somehow surprising, as the collective dynamics follows Crossover Collisions of Scroll Waves from the evolution of functional, i.e. infinite dimensional, equations. We discuss a few examples, where the collective The interaction of a pair of scroll waves is studied in a motion is chaotic and possibly even high-dimensional. Dis- chemical system by optical tomography. When the two lo- order in the form of diversity among the oscillator frequen- cally counter-rotating filaments approach each other closer cies (such as in the standard Kuramoto model) appears than radius of the spiral core, they may collide. These to be a basic ingredient, accompanied by the selection of crossover collisions lead to a rupture and a subsequent re- suitable phase response curves. The possible extension to connection of the filaments. Each reconnected filament phase-oscillators setups will be also discussed. consisted of parts that originated from both of the original Antonio Politi filaments. The conditions for rupture and reconnection of Institute for Complex Systems and Mathematical Biology, filaments will be discussed. University of Aberdeen, UK [email protected] Dennis Kupitz Institut of Experimental Physics [email protected] Ekkehard Ullner ICSMB, Department of Physics University of Aberdeen, UK Marcus Hauser [email protected] Institute of Experimental Physics Otto-von-Guericke-University, Magdeburg, Germany [email protected] MS72 Synchronization in a Cortical Multilayered Com- MS73 putational Model: A Simulation Study Role of Small Sized Heterogeneities in the Onset We performed a simulation study on the emergence of syn- and Perpetuation of Arrhythmias chronous states in a cortical network model. The model consists of excitatory and inhibitory neurons arranged in We investigate, in silico, the dynamics of rotors in 2D and four layers representing local cortical circuit. Neurons are in an anatomical model of human ventricles. We study the described by Izhikevich model with parameters that repro- effect of small size ionic heterogeneities, similar to those duce firing behavior of different excitatory and inhibitory measured experimentally. We show that they can anchor neuronal types. We studied versions of the model with- and also attract rotors rotating at a substantial distance out synaptic plasticity and with synaptic plasticity mod- from the heterogeneity. It depends on the extent of the eled by an asymmetric spike-timing-dependent plasticity heterogeneities and can be as large as 5-6 cm. We discuss (STDP) rule. The version without synaptic plasticity dis- possible mechanism of the observed phenomena. played asynchronous irregular spontaneous activity while the version with STDP displayed synchronous activity with Alexander Panfilov properties dependent on the neuronal types comprising the Department of Physics and Astronomy, Gent University network. Alexander.Panfi[email protected]

Antonio C. Roque, Renan O. Shimoura, Rodrigo F. O. Arne Defauw, Nele Vandersickel Pena Department of Physics and Astronomy Ghent Department of Physics, FFCLRP University,Belgium University of Sao Paulo, Ribeirao Preto, SP, Brazil [email protected], [email protected] antonior@ffclrp.usp.br, [email protected], rf- [email protected] Peter Dawyndt Department of Applied Mathematics, Computer Science MS72 and Statistics, Ghent University, Ghent Effects of Reciprocal Inhibitory Coupling in Syn- [email protected] chronous Neurons

The influences of chemical and electrical synapses are in- vestigated here using Hodgkin-Huxley model neurons. We MS73 study the dynamics displayed by a pair of neurons coupled Effects of Substrate Geometry on Spiral Wave Chi- 170 DS15 Abstracts

rality [email protected]

We introduced inexcitable obstacles into 1-cm-diameter cardiac monolayers, leading to the initiation of clockwise- MS74 rotating, counterclockwise-rotating, and pairs of spiral Oscillations in Neuronal Networks waves. Simulations demonstrated that the location of the obstacle and the side pacemaker frequency controlled spi- Neurons in the visual cortex exhibit heterogeneity in fea- ral wave chirality. Instabilities observed in action potential ture selectivity and the tendency to generate action po- duration restitution curves computed at different spatial tentials synchronously with other nearby neurons. Visual locations predicted sites of propagation failure, and, thus, responses from cat visual cortex during gamma oscillations spiral wave chirality. reveal a postive correlation between strength of oscillations, propensity towards synchronization, and sharpness of ori- Thomas D. Quail entation tuning. We present a model that can account for McGill University the correlations between these three properties and could [email protected] apply more generally to any brain region with analogous neuron types. Alvin Shrier, Leon Glass Stefanos Folias McGill University Department of Mathematical Sciences Department of Physiology University of Alaska Anchorage [email protected], [email protected] [email protected]

MS73 MS74 Scroll Waves in Viscous Systems with Stokes Flow: On a Kinetic Fitzhugh-Nagumo Equation Writing Filaments and Other New Tricks We consider the dynamics of the electric activity of a neu- Excitable and oscillatory reaction-diffusion systems can ron within a large network, described at a mesoscopic scale self-organize vortex states that rotate around one- incorporating intrinsic stochastic dynamics and disordered dimensional phase singularities. We have studied the dy- interactions. We are concerned with showing (i) existence namics of these scroll waves and filaments in the Belousov- and linear stability of steady states, as well as (ii) nonlinear Zhabotinsky reaction with a particular emphasis on the exponential stability in the weak connectivity regime. We interaction of filaments with internal heterogeneities and illustrate these results analyzing the electrically coupled the system boundaries. For a highly viscous system, scroll Fitzhugh-Nagumo kinetic equation. waves can be pinned to moving glass rods and repositioned at will. If the glass rod extends only along a fraction of Cristobal Quininao the filament, the free filament gets stretched out along the Laboratoire Jacques-Louis Lions rod trajectory and the trailing end moves with a speed [email protected] that depends on the local curvature. We also performed experiments on scroll wave drift along step-shaped height changes. Our experimental results are complemented by MS74 simulations of which some explicitly consider the Stokes Assembling Collective Activity in Neural Circuits flow generated by the slowly moving heterogeneities. Experimental breakthroughs are yielding an unprecedented Oliver Steinbock view of the brain’s connectivity and of its coherent dynam- Department of Chemistry and Biochemistry ics. But how does the former lead to the latter? We use Florida State University graphical and point process methods to reveal the contri- [email protected] bution of successively more-complex network features to coherent spiking.

Eric Shea-Brown MS74 Department of Applied Mathematics Dynamics of Networks with Partially Symmetric University of Washington Connectivity Matrices [email protected]

According to the long-standing Hebbian hypothesis, exter- nal stimuli are stored in long-term memory thanks to modi- MS75 fications of synaptic connectivity in neural circuits that are Entropy, Dissipation and Information Processing in activated by such stimuli. However, the details of synaptic Models of Complex Systems ‘learning rules’, as well as the impact of synaptic plastic- ity on network dynamics, are still unclear. In this talk, Recent advances in the study of (biological) complex sys- I will describe two complementary directions whose goal tems have shown an intimate connection between dissi- is to improve our understanding of these questions. The pation and computation. Information theory provides a first consists in investigating the effects of realistic ‘learn- universal framework to formalize these notions. In this ing rules’ that have been used to fit in vitro data on net- talk, I review complex systems as information-processing work dynamics. The second consists in inferring synaptic devices, which compute patterns at the expense of infor- ‘learning rules’ from the changes in neuronal activity upon mation written to hidden degrees of freedom. As an exam- repeated presentations of initially novel stimuli. ple, I review how such a picture yields a direct connection between the notions of dissipation used in the major mod- Nicolas Brunel elling paradigms of complex systems: Markovian stochastic Departments of Statistics and Neurobiology dynamics (stochastic thermodynamics, Monte-Carlo simu- The University of Chicago lations) and thermostatted equations of motion (molecular DS15 Abstracts 171

dynamics simulations). With an exactly solvable model, we discuss a possible work- ing mechanism of the demon. We draw a nonequilibrium Bernhard Altaner phase diagram and show that, depending on the location Max-Planck Insitute for Dynamics and Self-Organization on the diagram, the model can act either as an engine, con- [email protected] verting into work the extracted heat from the single heat source, or as a Landauer eraser, erasing information and consuming external work in the process. MS75 Degrees of Information Processing in Chaotic Dy- Dibyendu Mandal namical Systems University of California, Berkeley [email protected] It is well known that chaotic dynamical systems generate information. This is typically captured by the Kolmogorov- Sinai entropy, the supremum of Shannon entropy rates over MS76 all possible partitions of the system. We have recently Microfluidic Networks of Belousov-Zhabotinsky shown that this is a rather crude measure, and can in fact Drops be dissected in to two pieces: a part that is remembered by being correlated with future behavior, and a part which Several microfluidic based experimental systems of net- is forgotten and plays no role in the temporal evolution of works of non-linear chemical oscillators are presented. 2D the system. Here, we show that although the entropy rate planar arrays of oscillators with nearest neighbor coupling is invariant for both Markov and generating partitions of involving both inhibitory and excitatory species are devel- the system, its decomposition is not. We compare these oped. We explore phenomena such as synchronization, os- values for the tent map, and comment on what this means cillator death and assess the number of attractors, as well for study of such chaotic systems as information generators as their basin of attraction, as a function of the topology or processors. of the network and the heterogeneity of the oscillators and their coupling strength. Ryan G. James University of California, Davis Seth Fraden [email protected] Brandeis University Department of Physics [email protected] MS75 Time-Dependent Chaotic Attractors Shape Infor- mation Content in Neural Networks MS76 Synchronization and Network Topology of Electro- Large networks of sparsely coupled, excitatory and in- chemical Micro-Oscillators in On-Chip Integrated hibitory cells occur throughout the brain. They are re- Flow Cells sponsible for ongoing and complex computations, the ex- act mechanisms of which are poorly understood. Groups of We present that oscillatory reactions taking place on elec- connected neurons form very high-dimensional Dynamical trode arrays in single or branched flow channels inherently Systems that are often responding to rich, temporally fluc- form a network, whose characteristics can be tuned with tuating signals from various afferents. For many models the position of the electrodes. The network structure is of these networks, a striking feature is that their dynamics decoded from experimental measurements and the struc- are chaotic and thus, are sensitive to small perturbations. ture is interpreted with a theory. The unusual, spatially How does this chaos manifest in the neural code? Under- dependent network topology induces a unique dynamical standing how the dynamics of large driven networks shape response in the form of a spatial gradient in the extent of their capacity to encode and process information presents a synchronization with large set of electrodes. sizeable challenge. Inspired by this question, I will discuss the use of Random Dynamical Systems Theory as a frame- Istvan Z. Kiss, Yanxin Jia, Yifan Liu, Jasmine Coleman work to study information processing in high-dimensional, Department of Chemistry non-autonomous systems. Using a neural network model, Saint Louis University I will present recent results linking random strange attrac- [email protected], [email protected], [email protected], tors to noise entropy and input discrimination of dynamical [email protected] observables. Guillaume Lajoie MS76 Department of Applied Mathematics Synchronization in Networks of Coupled Chemical University of Washington Oscillators [email protected] We have studied heterogeneous populations of chemical os- cillators to characterize different types of synchronization MS75 behavior. The formation of phase clusters in stirred sus- Deconstructing Maxwells Demon pensions of Belousov-Zhabotinsky oscillators is described, where the (global) coupling occurs through the medium. The thermodynamic role of information processing has be- We then describe the formation of phase clusters and come an active topic of research because of its relevance chimera states in populations of photosensitive oscillators. to a wide range of problems, from bacterial sensing and The nonlocal coupling occurs via illumination intensity feedback control of microscopic systems to single-photon that is dependent on the state of each oscillator. The be- cooling of atoms. This is most dramatically captured in havior of oscillators in ring configurations as a function of the gedanken experiment of Maxwells demon, where a neat- the number of oscillators is described, including traveling fingered intelligent being can violate the second law of ther- cluster states. References: A. F. Taylor et al., Angewandte modynamics by extracting work from a single heat source. Chemie Int. Ed. 50, 10161 (2011); M. R. Tinsley et al., 172 DS15 Abstracts

Nature Physics 8, 662 (2012); S. Nkomo et al., Phys. Rev. Martin Wechselberger Lett. 110, 244102 (2013). University of Sydney [email protected] Kenneth Showalter West Virginia University Department of Chemistry MS77 [email protected] Singularities in Front Bifurcations with Scale Sep- aration

MS76 A paradigm for the occurrence of fronts are phase sepa- Long Transients to Synchronization in Random ration phenomena and Allen-Cahn type equations provide Networks of Electrochemical Oscillators the simplest model class. The coupling to further equa- tions with scale-separation leads to a surprisingly rich class In sparse, connected, random networks of attractively cou- of singularly perturbed problems that is amenable to anal- pled oscillators one can expect a range of dynamical equi- ysis. Over the past decades several methods have been libria, such as complete synchronization, phase synchro- developped to obtain rigorous existence and stability re- nization, partial synchronization or incoherence [Toenjes sults also for more complicated patterns than single fronts. et al., Chaos 20, 033108 (2010)]. Here we report on ex- In this talk we showcase an analysis of a three-component periments studying the transitions to and from a regime model with two linear equations coupled to an Allen-Cahn of phase synchronized electrochemical oscillators forming equation with scale separation. We show the front dynam- complex wave patterns on a small ring network with a few ics is organized by a butterfly catastrophe that leads to random non-local connections. accelerating and direction reversing slow fronts. In addi- tion, a more general result concerning the imbedding of Ralf Toenjes arbitrary singularities in such front bifurcations is shown. Potsdam University This is joint work with Martina Chirilus-Bruckner, Peter Dept. of Physics and Astronomy van Heijster and Arjen Doelman. [email protected] Jens Rademacher Michael Sebek University of Bremen Saint Louis University [email protected] Department of Chemistry [email protected] MS77 Istvan Z. Kiss Pinning and Unpinning in Nonlocal Equations Department of Chemistry Saint Louis University We investigate pinning regions and unpinning asymptotics [email protected] in nonlocal equations. We show that phenomena are re- lated to but different from pinning in discrete and inhomo- geneous media. We establish unpinning asymptotics using MS77 geometric singular perturbation theory in several examples. Travelling Waves and Canards in a Model of We also present numerical evidence for the dependence of Wound Healing Angiogenesis unpinning asymptotics on regularity of the nonlocal con- volution kernel. We discuss the existence of travelling waves in a singularly perturbed model of wound healing angiogenesis. We use Taylor Anderson geometric singular perturbation theory, supplemented with Mount Holyoke canard theory due to a fold in the critical manifold where [email protected] normal hyperbolicity is lost. Along this fold, canard points may exist that allow solution trajectories to pass through Gregory Faye the fold. These so-called canard solutions are crucial to Ecole´ des hautes ´etudes en sciences sociales establishing the existence of travelling waves, in particular, [email protected] that contain shocks. Arnd Scheel Kristen Harley University of Minnesota Queensland University of Technology School of Mathematics [email protected] [email protected]

Peter van Heijster David Stauffer Mathematical Sciences School Cornell University Queensland University of Technology dstauff[email protected] [email protected]

Robert Marangell MS77 The University of Sydney Canard Supersonique [email protected] Looking at the gas dynamics of stars under the assumption Graeme Pettet of spherical symmetry, I will show that transonic events Queensland University of Technology in such systems are canard phenomena – peculiar solu- School of Mathematical Sciences tion structures identified in geometric singular perturba- [email protected] tion problems. Consequently, stellar winds are carried by DS15 Abstracts 173

supersonic ducks, and canard theory provides a mathe- process from absolutely continuous to BV driving terms matical framework for this astrophysical phenomenon. So, through a continuity method [V. Recupero, Acontinuity whenever you have the chance to watch an aurora, remem- method for sweeping processes, J. Differential Equations, ber the superheros behind that scene – transonic canards! 2011]. We show that this method leads to a new of no- tion of sweeping process and we compare the two different dynamics. Martin Wechselberger University of Sydney Vincenzo Recupero [email protected] Department of Mathematics Politecnico di Torino, Italy [email protected] MS78 Control of Moreau’s Sweeping Process: Some Re- sults and Open Problems MS78 Estimation and Control Problems in Systems with While the existence theory is a very active area of research Moreau’s Sweeping Process since the ’70s, the understanding of the dynamics and of the control of the sweeping process is an entirely new sub- This talk will address control-theoretic design problems for ject. The talk will focus on some models and open prob- dynamical systems modeled as variants of Moreau’s sweep- lems, together with recent results, obtained in collabora- ing process. As a first case, we consider physical systems tion with other authors (including Nguyen D. Hoang, B. which comprise a time-varying Lipschitz vector field and Mordukhovich, R. Henrion), on necessary conditions for the set-valued mapping resulting from a first-oder convex various cases of optimal control for the sweeping process. sweeping process. A well-posedness result on existence and In particular, the case where the moving set depends on uniqueness of solutions for such systems is presented. The control parameters will be considered and the obtained nec- result is used for designing controllers, and state estima- essary conditions will be illustrated through examples. If tors in the context of output regulation problem. An ex- time permits also a minimum time problem will be ad- tension of these techniques is used to derive Lyapunov sta- dressed. bility conditions and design state estimators for systems involving sweeping processes with proximally regular set- Giovanni Colombo valued mappings. We next consider second order sweeping University Padova processes which are useful in modeling mechanical systems [email protected] with unilateral constraints. The problem of velocity esti- mation is considered using only the position measurements, which becomes nontrivial due to discontinuities in the ve- MS78 locity caused by the impacts. A state estimator is proposed On the Response of Sweeping Processes to Pertur- which has the form of a measure differential inclusion. It bation is shown that there exists a unique solution to the pro- posed differential inclusion and that solution converges to If x0 is an equilibrium of an autonomous differential equa-  the actual velocity of the system. tionx ˙ = f(x) and det f (x0) =0,then x0 persists un- der autonomous perturbations and x0 transforms into a Aneel Tanwani T -periodic solution under non-autonomous T -periodic per- Department of Mathematics turbations. In this paper we discover an analogues struc- University of Kaiserslautern, Germany tural stability for Moreau sweeping processes of the form [email protected] 2 −u˙ ∈ NB (u)+f0(u),u∈ R , i. e. we consider the sim- plest case where the derivate is taken with respect to the Lebesgue measure and where the convex set B of the re- MS79 2 duced system is an immovable unit ball of R . We show The Dynamics of Vortices and Masses over Surfaces that an equilibrium u0 = 1 persists under periodic per- of Revolution 2 turbations, if the projection f : ∂B → R of f0 on the tan- gent to the boundary ∂B is nonsingular at u0. Supported One of the today’s challenges is the formulation of the N- by RFBR grants 14-01-00867, 14-01-92004, 13-01-00347. body and N-vortex dynamics on Riemann surfaces. In this talk we show how the two problems are strongly related one Mikhail Kamenski another from the point of view of the intrinsic geometry Department of Mathematics, Voronezh State University of the surface where thedynamics takes place. Given a Universitetskaja pl. 1, Voronezh, 394006, Russia surface M of metric g and the distribution of matter S on [email protected] M, we deduce the dynamics of the masses and some of its properties. Oleg Makarenkov University of Texas at Dallas Stefanella Boatto [email protected] Dep. de Matematica Aplicada, IM Universidade Federal de Rio de Janeiro [email protected] MS78 Dynamics of Sweeping Processes with Jumps in the Gladston Duarte Driving Term P´os-Graduao do Instituto de Matem´atica Universidade Federal de Rio de Janeiro For discontinuous driving terms, sweeping processes were [email protected] originally formulated first for step multifunctions and then extended to BV moving convex sets. Another natural David G. Dritschel procedure consists in extending the classical continuous Department of Applied Mathematics 174 DS15 Abstracts

University of St Andrews Poincare-Birkhoff normal forms method near a relative [email protected] equilibrium on a fixed momentum level set.

Teresa J. Stuchi Cristina Stoica Instituto de Fisica Department of Mathematics Universidade Federal de Rio de Janeiro Wilfrid Laurier University [email protected] [email protected]

Carles Simo MS79 Departamento de Matematica i Analisi Universitat de Barcelona Studies on Dynamics of Vortices on a Flat Torus [email protected] In this talk I will present a complete description of the dynamics of two vortices on flat tori. The dynamics is de- Rodrigo Schaefer termined by a Hamiltonian equation for the evolution of Departament de Matem`atica Aplicada I An`alisi the center of vorticity with a Hamiltonian function defined ETSEIB-UPC in terms of Jacobi theta functions. We describe the bi- [email protected] furcation curves obtained under variations of the module parameter of the torus. The analysis of the stability for some special solutions are in progress. MS79 Eulerian Geometric Integration of Fluids for Com- Humberto H. de Barros Viglioni puter Graphics Departamento de Matematica Universidade Federal de Sergipe We present two geometric numerical methods for fluid sim- [email protected] ulation in computer animation. One is built to enforce Kelvin’s theorem in a semi-Lagragian manner, while the other is derived from first principles using a finite dimen- MS80 sional approximation of the group of volume-preserving Spiral Pinballs diffeomorphisms. The two resulting time integrators are shown to exhibit much improved numerical behavior. Time Spiral waves in excitable media possess both wave-like and permitting, we will also discuss extensions to magnetohy- particle-like properties. When resonantly forced, spiral drodynamics and geophysical flows. cores drift like particles along straight trajectories. These trajectories may reflect from medium boundaries or from Mathieu Desbrun obstacles within the medium. Interestingly, such reflections Dept. of Computing & Mathematical Sciences are almost always non-specular (that is, they have english), CALTECH and this results in interesting ricochet paths within the [email protected] medium. Paths may be further complicated if the medium itself undergoes motion. Dmitry Pavlov Department of Mathematics Jacob Langham Imperial College Mathematics Institute [email protected] University of Warwick [email protected] Evan S. Gawlik Stanford University Dwight Barkley [email protected] University of Warwick Mathematics Institute [email protected] Yiying Tong Computer Science and Engineering Michigan State University MS80 [email protected] Drift of Scroll Waves in Thin Layers Caused by Thickness Features Gemma Mason CMS dept. A scroll wave in a thin layer of excitable medium is sim- Caltech ilar to a spiral wave, but may drift depending on layer [email protected] geometry. Effects of sharp thickness variations are dis- tinct from filament tension and curvature-induced drifts Eva Kanso described earlier. We describe these effects asymptotically, University of Southern California with the layer thickness and its relative variation as small [email protected] parameters. Asymptotic predictions agree with numerical simulations for drift of scrolls along thickness steps, ridges, ditches, and disk-shaped thickness variations. MS79 Poincare-Birkhoff Normal Forms for Hamiltonian Irina Biktasheva Relative Equilibria University of Liverpool [email protected] Consider a cotangent bundle Hamiltonian system with a free, proper and compact Lie symmetry. We present Hans Dierckx an iterative algorithm suitable for the application of the Department of Physics and Astronomy DS15 Abstracts 175

Ghent University a level surface of an orthogonal coordinate system. A two- [email protected] term asymptotic expansion for the AMFPT is derived for an arbitrary N; it is compared with COMSOL numeri- Vadim N. Biktashev cal solutions. Steps are taken towards the derivation of College of Engineering, Mathematics and Physical higher-order asymptotics and a position-dependent MFPT Sciences formula. University of Exeter [email protected] Alexei F. Cheviakov Department of Mathematics and Statistics University of Saskatchewan MS80 [email protected] Tidal Forces Act on Cardiac Filaments Daniel Gomez During cardiac arrhythmias, scroll waves of electrical ac- University of British Columbia tivation rotate around a filament curve. By treating the [email protected] anisotropy of cardiac tissue as a curved space, I derive the laws of motion for filaments in anisotropic reaction- diffusion systems. In addition to the familiar filament twist MS81 and curvature terms, intrinsic curvature (Riemann curva- First Passage Times in Biological Self-Assembly ture terms) also act as tidal forces on the filament. Nucleation and self-assembly in biology usually involve a Hans Dierckx fixed number of constituents aggregating into clusters of Department of Physics and Astronomy a finite maximal size. Motivated by this scenario, we de- Ghent University rive the corresponding backward Kolmogorov equation for [email protected] the cluster probability distribution and study the distribu- tion of times it takes for a single maximal cluster to be completed, starting from any initial particle configuration. MS80 Surprisingly, we find, both analytically and numerically, Computation of Unstable Solutions of Cardiac that faster detachment can lead to a shorter mean time Models on Static and Evolving Domains to first completion of a maximum-sized cluster. This re- sult is due to the redistribution of trajectory weights upon Although typical cardiac models respect global Euclidean increasing the detachment rate so that paths that take a symmetries, these symmetries are generally broken by shorter time to complete a cluster become more likely. chaotic solutions. A generalized amplitude-phase represen- tation allows “decomposition’ of such chaotic multi-spiral Maria D’Orsogna solutions into tiles, each of which contains a single spiral CSUN described by an unstable periodic or relative periodic solu- [email protected] tion that respects translational and rotational symmetries locally. We present a method for computing such solutions Tom Chou on irregular domains with stationary or moving boundaries UCLA and discuss their properties. Departments of Biomathematics and Mathematics [email protected] Christopher Marcotte Georgia Institute of Technology [email protected] MS81 Signal Focusing Through Active Transport Roman Grigoriev Georgia Institute of Technology The precision of cellular signaling and novel diagnostic de- Center for Nonlinear Science & School of Physics vices is limited by the counting noise imposed by the ther- [email protected] mal diffusion of molecules. Many macromolecules and or- ganelles bind to molecular motors and are actively trans- ported. We will show that a random albeit directed de- MS81 livery of molecules to within a typical diffusion distance First-Passage Times of Random Walks in Confined to the receptor reduces the noise correlation time, thereby Geometries improving sensing precision. The conditions for improved sensing are compatible with observations in living cells. Abstract not available. Aljaz Godec Olivier Benichou Universit¨at Potsdam Universite Pierre et Marie Curie [email protected] [email protected] Ralf Metzler Inst for Physics & Astronomy MS81 University of Potsdam Asymptotic Analysis of Narrow Escape Problems [email protected] in Non-Spherical 3D Domains

Narrow escape problems for non-spherical 3D domains with MS82 N ≥ 1 boundary traps are considered. We compute an Control of Multiscale Dynamical Systems asymptotic expression for the average mean first passage time (AMFPT) for three-dimensional domains bounded by New applications in materials, medicine, and computers 176 DS15 Abstracts

are being discovered where the control of events at the trary positive smooth function. This also motivates the de- molecular and nanoscopic scales is critical to product qual- sign of circuits that harvest energies contained in infinitesi- ity, although the primary manipulation of these events dur- mal oscillations of ambient electromagnetic fields. To over- ing processing occurs at macroscopic length scales. These come a key obstacle, which is to compensate the dissipa- systems motivate the creation of tools for the control of tive effects due to finite resistances, we propose a theory multiscale systems that have length scales ranging from the that quantifies how small/fast periodic perturbations affect atomistic to the macroscopic. This talk describes a system- multidimensional systems. This results in the discovery of atic approach that consists of stochastic parameter sensi- a mechanism that reduces the resistance threshold needed tivity analysis, Bayesian parameter estimation applied to for energy extraction, based on coupling a large number of ab initio computational chemistry calculations and experi- RLC circuits. mental data, model-based experimental design, hypothesis mechanism selection, and multistep optimization. The ap- Molei Tao plication of control theory to the analysis and design of Courant Institute, NYU multiscale simulation codes is also discussed. [email protected]

Richard D. Braatz Massachusetts Institute of Technology MS83 Department of Chemical Engineering Nonlinear Waves in Microsphere-Based Metamate- [email protected] rials

Locally-resonant metamaterials and granular media are MS82 both highly dispersive and known to drastically affect Some Results on the Backward Stability of Singular acoustic wave propagation. In this work, we consider Perturbation Approximations of Linear and Non- the nonlinear dynamics of a system at the intersection of linear Stochastic Control Systems these two types of media: a locally-resonant metamaterial composed of microscale spheres adhesively coupled to an An important aspect of model reduction of large-scale con- elastic substrate, where the spheres act as nonlinear local trol systems is the estimation of the approximation error resonators. Dynamical simulations of a discrete element as a function of the control input. A different question is model representing the metamaterial are compared with whether feedback controls computed from a reduced model photoacoustic experimental measurements. are a reasonable approximation of the optimal control for the original model, the computation of which is often infea- Nicholas Boechler sible. In this talk we present recent results on the backward University of Washington stability of singular perturbation approximations of a cer- Department of Mechanical Engineering tain class of stochastic control systems and discuss various [email protected] applications.

Carsten Hartmann MS83 Freie Universit¨at Berlin (Free University of Berlin) Multiscale Analysis of Strongly Localized Waves [email protected] Abstract not available.

MS82 Guillaume James Variational Integrators for Multiscale Dynamics Laboratoire Jean Kuntzmann, Universit´e de Grenoble and CNRS In this talk variational integrators are developed for the INRIA Grenoble structure-preserving integration of systems with dynamics [email protected] on multiple time scales. The construction is based on a derivation in closed form via a discrete variational prin- ciple on a time grid consisting of macro and micro time MS83 nodes. The structure preserving properties as well as the Standing Waves on Tadpole Graphs convergence behavior of the multirate integrator are ana- lyzed and its performance is demonstrated by numerical We develop a detailed rigorous analysis of edge bifurcations examples. of standing waves in the nonlinear Schrodinger (NLS) equa- tion on a tadpole graph (a ring attached to a semi-infinite Sina Ober-Bloebaum line subject to the Kirchhoff boundary conditions at the Universit¨at Paderborn (University of Paderborn) junction). It is shown in the recent work of C. Cacciapuoti, [email protected] D. Finco, and D. Noja by using explicit Jacobi elliptic func- tions that the cubic NLS equation on a tadpole graph ad- Sigrid Leyendecker mits a rich structure of standing waves. Among these, there University of Erlangen-Nuremberg are different branches of localized states bifurcating from [email protected] the edge of essential spectrum of an associated Schrodinger operator. In this work, joint with D. Noja (Milan), we show by using the Lyapunov-Schmidt reduction that the bifurca- MS82 tion phenomenon is general for other power nonlinearities Control of Oscillators, Temporal Homogenization, and moreover, the local properties of bifurcating standing and Energy Harvest by Super-Parametric Reso- waves can be characterized in full details. We distinguish nance a primary branch of never vanishing standing waves bifur- cating from the trivial solution and an infinite sequence of We show how to control an oscillator by periodically per- higher branches with oscillating behavior in the ring. The turbing its stiffness, such that its amplitude follows an arbi- higher branches are not small at threshold and bifurcate DS15 Abstracts 177

from the branches of degenerate standing waves with van- network coupled with lateral inhibition. We then compute ishing tail outside the ring. Each higher nontrivial branch the traveling pulses using a system of equivalent delayed breaks the symmetry of the degenerate branch. Moreover, differential equations derived from the neural field model. we analyze stability of bifurcating standing waves. Namely, We further study the dynamical dependency of traveling we show that the primary branch is composed by orbitally pulses on the gain and coupling parameters, and demon- stable standing waves, while the nontrivial higher branches strate how to determine the stability of given traveling are linearly unstable near the bifurcation point. The sta- pulses. bility character of the degenerate branches remains incon- clusive at the analytical level, whereas heuristic arguments Yixin Guo and numerical approximations support the conjecture of Drexel University their linear instability at least near the bifurcation point. Department of Mathematics [email protected] Dmitry Pelinovsky McMaster University Aijun Zhang Department of Mathematics Department of Mathematics [email protected] Drexel University [email protected] MS83 Granular Acoustic Switches and Logic Elements MS84 Homogenization Theory for Neural Field Models We present analytical, numerical, and experimental demonstration of an acoustic switch, analogous to its elec- This talk is divided into two parts. In the first part we tric/optical counterpart, based on a 1D chain of granular review the derivation of the homogenized one - population crystals. This system controls the propagation of primary Amari equation by means of two - scale convergence tech- output stress waves by applying secondary control waves, nique in the case of periodic microvariation in the connec- exploiting the nonlinear dynamic effects of the granular tivity function. In the second part we discuss the existence chain. We also realize OR and AND acoustic logic gates and stability of single and multibump solutions of the ho- using multiple control signals. mogenized model.

Jinkyu Yang,FengLi John Wyller University of Washington Department of Mathematical Sciences and Technology [email protected], [email protected] Norwegian University of Life Sciences [email protected] Paul Anzel California Institute of Technology [email protected] MS84 Asymmetric Stationary Bumps in Neural Field Panayotis Kevrekidis Models University of Massachusetts [email protected] For 1D neural field models, we show that the symmetry of the connectivity function causes a degeneracy, permitting Chiara Daraio the existence of asymmetric bump solutions. When the ETH Z¨urich, Switzerland and California Institute of Tech governing nonlinear integral equation is transformed into [email protected] a higher-order ODE, the degeneracy leads to a conserved quantity. With this, we construct a horseshoe map and obtain infinitely many asymmetric/symmetric bump solu- MS84 tions. We then discuss the persistence of these solutions Modulating Synaptic Plasticity Within In Vitro under perturbations of the connectivity function and the Hippocampal Networks nonlinear gain.

Synaptic plasticity, in the form of long-term potentiation Dennis Yang (LTP) and long-term depression (LTD), is thought to un- Department of Mathematics derlie learning and memory. Both must be highly regulated Drexel University for proper memory storage to take place. We chemically [email protected] induce LTP and LTD within networks of hippocampal neu- rons and quantify the changes in action potential firing within the purview of network dynamics. MS85 Contact Network Models for Immunizing Infec- Rhonda Dzakpasu tions Georgetown University Department of Physics Many infectious agents spread via close contact between [email protected] infected and susceptible individuals. The nature and struc- ture of interactions among individuals is thus of fundamen- tal importance to the spread of infectious disease. Het- MS84 erogeneities among host interactions can be modeled with Traveling Patterns in Lateral Inhibition Neural contact networks, and analyzed using tools of percolation Networks theory. Thus far, the field of contact network epidemiology has largely been focused on the impact of network struc- We investigate the necessary condition- asymmetry in the ture on the progression of disease epidemics. In this talk, coupling function, for traveling pulses to exist in a neural we introduce network models which incorporate feedback 178 DS15 Abstracts

of the disease spread on network structure, and explore how methods—such as Wolbachia—and vaccines. In this talk, this feedback limits the potential for future outbreaks. This I will discuss mathematical modeling that is being used to has implications for seasonal diseases such as influenza, and help design dengue control efforts using one, or a combina- supports the need for more adaptive public health policies tion, of these methods. in response to disease dynamics. Alun Lloyd Shweta Bansal North Carolina State University Penn State University alun [email protected] [email protected]

MS86 MS85 Experimental Studies of Burning Invariant Mani- Mathematical Models of the Spatial and Evolution- folds as Barriers to Reaction Fronts ary Dynamics of Influenza A We study Belousov-Zhabotinsky reaction fronts in the fol- The research areas of population biology and dynamical lowing flows: (a) a single vortex flow; (b) a chain of oscil- systems already have a fruitful shared history. Within this, lating vortices; and (c) extended vortex array or spatially disease modelling has been particularly lively for both its disordered flows. In these flows, front propagation is im- rich dynamics and its practical importance. In this talk, peded and sometimes pinned by burning invariant mani- we will have a brief tour of some of the types of models that folds (BIMs) which act as one-way barriers. Experimental are in use for both the spatial and evolutionary aspects of measurements of barriers are compared with BIMs that are the spread of influenza at the population level, and some predicted numerically. We consider the limits of validity of of the future mathematical challenges. the BIM approach to more complicated flows.

Julia R. Gog Savannah Gowen Department of Applied Mathematics and Theoretical Mount Holyoke College Physics 50 College Street, South Hadley, MA 01075 University of Cambridge [email protected] [email protected] Tom Solomon Bucknell University MS85 [email protected] A Multi-Scale Model of Multiple Exposures to a Pathogen MS86 Dose size and incubation period length are related for many Front Pinning in Single Vortex Flows infectious diseases. We explore a dose-dependent latent period of infection (a component of incubation period) fol- We study fronts propagating in 2D fluid flows and show lowing multiple exposures to a pathogen, and study its ef- that there exist stable invariant front configurations for fect on disease transmission in a population. The immuno- fairly generic flows. Here we examine the simple flow which epidemiological model is developed using a threshold-type combines a single vortex with an overall wind. Existence delay, which is transformed in a biologically natural way, to of the stable front is related to the underlying fluid bifurca- a system of differential equations with state-dependent de- tion. This elementary structure has application in chemical lay. Bistability results, which has implications in infection reactor beds and laminar combustion in well-mixed fluids. control.

Jane Heffernan John R. Mahoney Centre for Disease Modelling, Mathematics & Statistics University of California, Merced York University [email protected] jmheff[email protected] Kevin A. Mitchell Redouane Qesmi University of California, Merced York University Physics [email protected] [email protected]

Jianhong Wu Department of Mathematics and Statistics MS86 York University Propagation of An Autocatalytic Reaction Front in [email protected] Heterogeneous Porous Media

We investigate experimentally and numerically the cou- MS85 pling of the propagation of an auto-catalytic reaction and Evaluation of Combined Strategies for Controlling the flow in porous media. We will investigate the different Dengue Fever propagation modes depending on the flow direction, its am- plitude and the disorder of the medium. More particularly, Dengue is the most significant mosquito-borne viral infec- we will demonstrate that heterogeneity of the medium in- tion of humans, causing 50-100 million infections annually. duces a rich variety of front dynamic and morphology. The main line of attack against dengue has been traditional mosquito control measures, such as insecticides. The com- Laurent Talon ing years will see the broadening of our anti-dengue arse- Univ. Paris-Sud nal to include genetically-modified mosquitoes, biocontrol Orsay, F-91405, France DS15 Abstracts 179

[email protected] the two vector fields. Thus, we then construct and discuss different smooth reformulations of the model and compare Dominique Salin model predictions with data on freshwater plankton. lab. FAST, UMPC [email protected] Sofia Piltz University of Oxford sofi[email protected] MS86 Front Propagation in Cellular Flows for Fast Reac- tion and Small Diffusivity MS87 We investigate the influence of cellular flows on the propa- Infinitely Many Coexisting Attractors in the gation of Fisher-Kolmogorov-Petrovsky-Piskunov chemical Border-Collision Normal Form fronts in the limit of small molecular diffusivity and fast reaction i.e., large P´eclet (Pe)andDamk¨ohler (Da)num- The nature of piecewise-linear maps (such as the tent map) bers. We develop an asymptotic theory that describes the facilitates exact calculations, yet such maps can display front speed in terms of a periodic path – an instanton – extremely complicated dynamics (including chaos). This that minimizes a certain functional and yields closed-form talk looks at two mechanisms by which two-dimensional results for (log Pe)−1 Da Pe and Da Pe.Our piecewise-linear continuous maps can exhibit infinitely theoretical predictions are compared with (i) numerical so- many stable, or asymptotically stable, periodic solutions lutions of an eigenvalue problem and (ii) simulations of the at special points of parameter space. Scaling laws indi- advection–diffusion–reaction equation. cate the rate at which the number of coexisting attractors decreases with the distance from these points. Alexandra Tzella, Jacques Vanneste School of Mathematics David J. Simpson University of Edinburgh Institute of Fundamental Sciences [email protected], [email protected] Massey University [email protected] MS87 Geometric Optics and Piecewise Linear Systems MS88 Light through a chessboard material with two different re- Swarming of Self-propelled Particles in Fluids fractive indices (for black and white squares) is refracted and reflected in complicated ways. I will describe the Self propulsion, a distinction between active swarmers and derivation of a return map for a geometric ray obeying passive interacting particles, often invokes speed regula- Snell’s Law and use this to derive properties of the rays. tion strategies that can be essential for a swarm to develop and maintain a certain flocking formation. However, speed Paul Glendinning regulation depends on the ability of a swarmer to sense its University of Manchester own speed relative to its perceived surroundings. Here we [email protected] study a swarming system in low-Reynolds number flows, examining the effects of hampered speed regulation by the disturbance flow on flock formations. MS87 Analysis of Traveling Pulses and Fronts in a Nons- Yaoli Chuang mooth Neural Mass Model California State University, Northridge We study the activity of coupled populations of excitatory [email protected] and inhibitory neurons in a neural firing rate model that in- cludes 1D nonlocal, spatial coupling. To facilitate analysis Maria D’Orsogna of spatio-temporal patterns, we approximate the (typically CSUN smooth) nonlinear firing rate function with the Heaviside [email protected] step function. We study the corresponding nonsmooth dif- ferential system in traveling wave coordinates, with a par- ticular interest in how the system transitions from traveling MS88 front to pulse as the time-constant of inhibition increases. Origin and Structure of Dynamic Social Networks Based on Cooperative Actions Jeremy D. Harris Department of Mathematics Societies are built on social interactions. A novel theoret- University of Pittsburgh ical framework to model dynamic social networks focusses [email protected] on individual actions instead of interactions between indi- viduals and thereby eliminates the traditional dichotomy between the strategy of individuals and the structure of MS87 the population. As a consequence, altruists, egoists and Are Plankton Discontinuous, Smooth Or Slow-Fast fair types are naturally determined by the local social (and Furious)? structures, while globally egalitarian networks or stratified structures arise. Cooperative actions drive the emergence In this talk, we first discuss a piecewise-smooth dynamical and shape the structure of social networks. system constructed for one predator feeding on two differ- ent types of prey and inspired by plankton observations. Christoph Hauert,LucasWardil The piecewise-smooth model has a discontinuity between The University of British Columbia 180 DS15 Abstracts

[email protected], [email protected] to Probe Network Structure

We apply the Moore-Shannon network reliability polyno- MS88 mial to infectious disease epidemiology on large social net- Hotspots in a Non-Local Crime Model works. Special cases of the polynomial represent the prob- ability of cascading failures or epidemic outbreaks in com- We extend the Short et al. burglary hotspot model to allow plex networks. Although its exact evaluation is NP-hard, for a larger class of criminal movement. Specifically, we efficient, scalable Monte-Carlo estimation is practical. A allow criminals to travel according to a L´evy flight rather physical interpretation supports analytical understanding than Brownian motion. This leads to a non-local system of how local structures interact with dynamics to produce of differential equations. The stability of the homogeneous global function. state is studied both numerically and through a Turing- type analysis. The hotspot profiles are then constructed to Stephen Eubank leading order in a singular regime. Virigina Bioinformatics Institute, VA Tech [email protected] Scott Mccalla Montana State University Yasamin Khorramzadeh [email protected] Physics Dept. Virginia Tech Jonah Breslau [email protected] Pomona College [email protected] Mina Youssef Virginia Bioinformatics Institute Sorathan Chaturapruek Virginia Tech Harvey Mudd College [email protected] tum [email protected] Shahir Mowlaei, Madhurima Nath Theodore Kolokolnikov Physics Dept. Dalhousie University Virginia Tech [email protected] [email protected], [email protected]

Daniel Yazdi University of California, Los Angeles MS89 [email protected] Dynamical Macro-Prudential Stress Testing Using Network Theory

MS88 We present a dynamic model to reveal the systemic struc- Co-Dimension One Self Assembly ture of a banking system, to analyze its sensitivity to ex- ternal shocks and to evaluate the presence of contagious Self assembly refers to emergent behavior that oc- underlying features of the system. As a case study, we curs in systems with a large number of interacting make use of the Venezuelan banking system in the period molecules or nanoparticles. These systems produce or- of 1998–2013. The introduced model was able to capture, dered, supramolecular structures solely due to the interac- in a dynamic way, changes in the structure of the system tions between their constituent molecules or particles. My and the sensitivity of banks portfolio to external shocks. talk will focus on mathematical models for physical pro- Results suggest the fruitfulness of this kind of approach to cesses, such as the assembly of inorganic polyoxometalate policy makers and supervision agencies to address macro- (POM) macroions into hollow spherical structures or the prudential dynamical stress testing and regulation. assembly of surfactant molecules into micelles and vesicles, where the supramolecular structure has co-dimension one Dror Y. Kenett characteristics. I will discuss both the mathematical the- Boston University, Physics Department ory that characterizes when such structures can arise, as [email protected] well as applications of these insights to physical models of these assemblies. MS89 James von Brecht Role of Netwok Topology in Collective Opinion California State University, Long Beach Formation [email protected] To investigate the role of network structures on the phe- nomena of collective opinion formation, we investigate sev- Scott Mccalla eral modifications to the voter model on co-evolving net- Montana State University works. For example we modify the rewiring step by a path- [email protected] length-based preference for rewiring that reinforces local clustering and show that reinforcement of clustering in a David T. Uminsky voter model can have significant ramifications. Further- University of San Francisco more, we will be employing this voter model dynamics to Department of Mathematics analyze the structures of various empirical social network [email protected] data sets.

Nishant Malik MS89 Department of Mathematics Network Reliability As a Tool for Using Dynamics University of North Carolina at Chapel Hill, NC, USA DS15 Abstracts 181

[email protected] tic tools do not readily apply to epistemic uncertainty quantification since probability distributions may not be available. In this paper, we propose a general three-step MS89 procedure based on fuzzy set theory to deal with epistemic Linear Dynamics on Brain Networks: A Tool for uncertainty and extend it for mixed epistemic and aleatory Understanding Cognition uncertainty quantification. The convergence rate of ob- tained numerical solutions is analyzed and demonstrated Human cognitive function is a complex phenomenon that with examples. occurs via intricate neuronal dynamics evolving over a sculpted anatomical network architecture housed within YanYan He the skull. Yet, fundamental structural drivers of these Scientific Computing and Imaging Center functions remain poorly understood. Drawing inspiration University of Utah from network control theory, here we utilize a simple lin- [email protected] ear model of brain dynamics on experimentally measured anatomical networks to predict the role of brain areas (net- work nodes) in moving the brain into (i) easily reachable Dongbin Xiu states, (ii) difficult-to-reach states, and (iii) states that University of Utah require interactions between network communities, which [email protected] traditionally map to cognitive systems including audition, vision, and motor systems. Our predictions map well to known functions of brain areas, suggesting that structural MS90 network architecture forms a fundamental constraint on Using Sensitivity Analysis to Understand S. aureus observed cognitive processes underlying human thought. Infections More broadly, our study illustrates the utility of dynamic models on networks to uncover critical drivers of system function. The immune system is a complex network of interactions that challenges the technology and skills of biologists and Danielle Bassett mathematicians who study it. We present results from School of Engineering and Applied Science global sensitivity analysis techniques (PRCC and Sobol’) University of Pennsylvania for two different models, one ODE and one PDE, and dis- [email protected] cuss the usefulness of these results for: model reduction, understanding immune system interactions, focusing data Fabio Pasqualetti assimilation techniques on parameters of interest, and mo- Department of Mechanical Engineering tivating biological experiments in the context of S. aureus University of California, Riverside, CA infections. [email protected] Angela M. Jarrett Florida State University MS90 Department of Mathematics The Dynamics of Alopecia Areata [email protected]

Alopecia areata is an autoimmune disease causing distinct Nick Cogan, M Yousuff Hussaini patterns of hair loss. Little is known regarding the causes Florida State University or treatment of the disease. We develop an ODE model [email protected], [email protected] for alopecia areata dynamics which incorporates one of the current hypotheses that explains a range of experimental observations and suggests several avenues for treatment. Sensitivity analysis is used to determine which inputs have MS90 the greatest influence helping focus the study on avenues Computational Aspects of Stochastic Collocation with the highest potential impact. with Multi-Fidelity Models Atanaska Dobreva Florida State University We shall discuss a numerical approach for the stochas- [email protected] tic collocation method with multifidelity simulation mod- els. The method combines the computational efficiency Ralf Paus of low-fidelity models with the high accuracy of high- University of Manchester fidelity models. We shall illustrate the advantages of the University of M¨unster method via a set of more comprehensive benchmark ex- [email protected] amples including several two-dimensional stochastic PDEs with high-dimensional random parameters. Finally, We suggest that tri-fidelity simulations with a low-fidelity, a Nicholas Cogan medium-fidelity, and a high-fidelity model would be suffi- Florida State University cient for most practical problems. [email protected] Xueyu Zhu MS90 Scientific Computing and Imaging Center Epistemic Uncertainty Quantification Using Fuzzy University of Utah Set Theory [email protected]

Epistemic uncertainty due to lack of knowledge is in- Dongbin Xiu evitable in modeling and simulation. The existing stochas- University of Utah 182 DS15 Abstracts

[email protected] [email protected]

MS91 MS91 Moreau Sweeping Processes on Banach Spaces Evolution Equations Governed by Sweeping Pro- cesses and Applications in Heat Equations with The sweeping process or Moreau’s process in a Hilbert Controlled Obstacles space H (introduced and studied by J.J. Moreau in J.D.E. in 1977) is an interesting problem in both Analysis and In this talk, we provide results on existence, stability and Mechanics optimality conditions for the following class of evolution equations −y˙(t) ∈ N(C(t); y(t)) a.e. in [0,T],y(0) = y0 ∈ C(0) −x˙(t) ∈ ∂Φ(x(t))+N(x(t); C(t, u(t))) a.e. t ∈ [0,T]; x(0) = x0. where C(t) is a closed convex moving set depending on the time t ∈ [0,T]andy :[0,T] → H is a BV mapping. There We then apply these results for heat equations with con- are a plethora of variants in this problem in Hilbert spaces. trolled obstacles. This talk bases on joint work with Juan In this talk I will present my last recent results on the ex- Peypouquet and Luis M. Brice˜no-Arias. istence of solutions for several extensions to Banach spaces Hoang Nguyen of Moreau sweeping processes and its variants. The main Department of Mathematics problems that will be presented are: For a given reflexive University of Technical Federical Santa Maria, Chile smooth Banach space X, [email protected] (P 1) Find y :[0,T] → X∗ such that ⎧ − d ∈ ∗ ∗ MS91 ⎨ dt (y(t)) N(C(t); J (y(t))) + F (t; J (y(t))) a.e. in [0,T]and Sweeping Process and Congestion Models for ⎩ J ∗(y(t)) ∈ C(t), ∀t ∈ [0,T], and J ∗(y(0)) ∈ C(0). Crowd Motion

(P 2) Find y :[0,T] → X∗ such that We propose a mathematical model of crowd motion in ⎧ emergency evacuation. This microscopic model takes into ⎨ −y(t) ∈ N(C(t); J ∗( d (y(t)))) + F (t; J ∗(y(t))) a.e. in [0,Taccount]and the local interactions between pedestrians. The dt underlying evolution problem takes the form of a first order ⎩ ∗ d ∗ differential∗ d inclusion.and its well-posedness can be proved J ( (y(t))) ∈ C(t), a.e. on [0,T], and J (y(0)) ∈ C(0),J ( y(0)) ∈ C(0). dt withdt the help of recent results concerning sweeping process ∗ by uniformly prox-regular sets. Furthermore, we propose (P 3) Find y :[0,T] → X such that a numerical scheme (adapted from Moreau’s catching-up ⎧ − d ∈ ∗ ∗ algorithm) and prove its convergence. ⎨ dt (y(t)) N(C(t, J (y(t))); J (y(t))) a.e. in [0,T]and

⎩ ∗ ∗ ∗ Juliette∗ Venel J (y(t)) ∈ C(t, J (y(t))), ∀t ∈ [0,T], and J (y(0)) ∈ C(0,JLab(y de(0))) Mathematiques. et leurs Applications de Valenciennes Here J ∗ is the normalized duality mapping in X∗ defined ∗ Universite Lille-Nord de France from X to X by [email protected] ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ 2 ∗ ∗ 2 J (x )={j (x ) ∈ X : x ,j (x ) = j (x )x  = x  = j (x ) }. MS92 Braid Dynamics, Self-organized Criticality, and So- Messaoud Bounkhel lar Coronal Heating Department of Mathematics King Saud University, Saudi Arabia Magnetic field lines in the atmosphere of the sun are an- [email protected] chored at the surface, and exist in a highly conducting environment. Hence their topological structure can only change gradually via surface motions, or violently via flar- MS91 ing events. We present models for the evolution of the braid Periodic Solutions of Moreau Sweeping Processes structure to a self-organized state. The discrete nature of and Applications the flux distribution at the surface enhances the resulting energy dissipation. The concept of equilibrium has been introduced by O. Makarenkov in recent studies of the following autonomus Mitchell Berger Moreau sweeping process: Department of Mathematics University of Exeter  −u (t) ∈ NB (u(t)) + f(u(t)). [email protected]

In the case of periodically perturbed f there exists a so- lution in the neighbourhood of the equilibrium. By using MS92 contraction mapping theory it is possible to prove stabil- Characterizing Complexity of Aperiodic Braids of ity of closed orbit for a prototypic sweeping process in a Trajectories Hilbert space. A braid of trajectories is an algebraic model of the se- Ivan Gudoshnikov quence of interchanges of particles advected by a flow. In- Department of Mathematical Sciences sights based on braid-theoretic arguments typically require University of Texas at Dallas periodicity of analyzed trajectories. This talk explores DS15 Abstracts 183

what can be deduced from generic, non-periodic trajecto- [email protected] ries sampled from a flow. We define an aperiodic quantifier of braid complexity and present its dependence on flow pa- Humberto Ocejo rameters, on number of trajectories analyzed, and discuss Universidad de Sonora connections to topological entropy. [email protected] Marko Budisic University of Wisconsin-Madison MS93 Department of Mathematics [email protected] Interaction of Electric Field Stimuli with Scroll Waves in Three Dimensions

Jean-Luc Thiffeault An applied electric field interacts differently with an action Dept. of Mathematics potential scroll wave depending on its orientation with the University of Wisconsin - Madison scroll wave’s filament. In particular, defibrillation charac- [email protected] teristics of the electric field are often more favorable when oriented parallel to the filament, particularly in the case of a thin medium. Theory and computer simulations will MS92 be presented illustrating the dynamics of the scroll-wave- Topological Shocks in Burgers Turbulence electric-field interaction and its dependence on wall thick- nessandfieldorientation. We shall discuss statistical properties of global solutions to the random forced Burgers equation. The problem is Niels Otani closely related to analysis of minimizers for random time- Rochester Institute of Technology dependent Lagrangian systems. We show that for such [email protected] systems on compact manifolds there exists a unique global minimizer. We also discuss dynamical properties of shocks and show that their global structure is quite rigid and re- Valentin Krinski flects the topology of the configuration manifold INLN,CNRS, France [email protected] Kostantin Khanin Department of Mathematics University of Toronto MS93 [email protected] Describing Scroll Wave Ring Interactions Via In- teracting Potentials

MS92 We study the dynamics of scroll rings using a simplified Topology of Vortex Trajectories in Wake-Like model of cardiac action potential (the Karma model) that Flows produces scroll waves with circular core at high excitability (positive tension regime). We calculate the trajectories of Complex vortex patterns can emerge downstream of bluff symmetric scroll rings as a function of core radius and dis- bodies as the result of fluid-structure interaction. As in tance to a bottom boundary and derive a potential function many fluid systems, the vortex cores define regions that that can then be used to characterize and predict the dy- remain coherent for relatively long times. Using a reduced- namics without the need for integrating the whole system. order model of the dynamics, the topological complexity of the flow is examined through braiding of the vortex trajec- tories. This wake-like model provides an example of how Flavio M. Fenton topological chaos may occur naturally through the dynam- Georgia Institute of Technology ics of coherent structures. fl[email protected]

Mark A. Stremler Jairo Rodriguez Biomedical Engineering and Mechanics Universidad de Sonora Virginia Tech [email protected] [email protected] Daniel Olmos MS93 Department of Mathematics Universidad de Sonora On the Generation of Spiral and Scroll Waves by [email protected] Periodic Stimulation of Excitable Media in the Presence of Obstacles of Minimum Size In this work we consider the periodic stimulation of two MS93 and three dimensional excitable media in the presence of Unusually Simple Way to Create Spiral Wave in obstacles. We focus our attention in the understanding of An Excitable Medium the minimum size obstacles that allow generation of spiral and scroll waves, and describe different mechanisms that Our analytical and numerical results indicate that a suffi- lead to the formation of such waves. The present stud- ciently strong jump in the diffusion coefficient can result ies might be helpful in understanding and controlling the in a unidirectional propagation block in a nonuniform ex- appearance of spiral and scroll waves in the medium. citable medium. This phenomenon can be used to create spiral wave in a two-dimensional medium with a specific Daniel Olmos size and geometry of the inhomogeneity. Following this Department of Mathematics way the spiral wave can be created simply after a single Universidad de Sonora excitation stimulus while others known methods need at 184 DS15 Abstracts

least two stimuli. corresponding expansions of the first passage time density for the diffusing molecule to find the target. Vladimir Zykov,AlexeiKrekhov Max Planck Institute for Dynamics and Self-Organization Jay Newby [email protected], [email protected] Mathematical Biosciences Institute The Ohio State University Eberhard Bodenschatz [email protected] Max Planck Institute for Dynamics & Self-Organization [email protected] MS94 Drunken Robber, Tipsy Cop: First Passage Times, MS94 Mobile Traps, and Hopf Bifurcations Narrow Escape to Traps with Absorbing and Re- For a random walk on a confined one-dimensional domain, flecting Portions we consider mean first passage times in the following two We study the Narrow Escape Problem to a small trap with scenarios: a randomly moving trap and an oscillating trap. a mixed configuration of absorbing and reflecting sections. In both cases, we find that a stationary trap actually per- In the limit of small trap radius, we derive a high order ex- forms better than a very slowly moving trap; however, a pansion for the mean survival time which incorporates the trap moving sufficiently fast performs better than a sta- asymmetry of the trap through an orientation term. The tionary trap. Also, we will show the connection between orientation of the trap is found to significantly influence MFPT and Hopf-bifurcation in Gray-Scott model. capture time, particularly in the scenario where the trap is Justin C. Tzou undergoing prescribed motion. Dalhousie University Alan E. Lindsay [email protected] Applied Computational Mathematics and Statistics University of Notre Dame Shuangquan Xie [email protected] Mathematics and Statistics Dalhousie University [email protected] MS94 Sampling First-Passage Events When Drift Is In- Theodore Kolokolnikov cluded in the First-Passage Kinetic Monte Carlo Dalhousie University Method [email protected]

We have developed a method for simulating stochastic reaction-drift-diffusion systems, where the drift arises from MS95 potential fields. The method combines elements of the A Dynamical Switching of Reactive and Nonreac- First-Passage Kinetic Monte Carlo (FPKMC) method for tive Modes at High Energies reaction-diffusion systems and the Wang-Peskin-Elston lat- tice discretization of drift-diffusion. The original FP- In Hamiltonian systems, the reaction coordinate, the de- KMC uses analytic solutions of the diffusion equation and gree of freedom along which reaction proceeds, has been therefore cannot include nonlinear drift. In our method considered to be unchanged independent of the total en- (Dynamic Lattice FPKMC), each molecule undergoes a ergy of the system. I will present our recent finding that, continuous-time random walk on its own adaptive lattice. for more than two degrees of freedom Hamiltonian systems, the identity of reaction coordinate can change, in general, Ava Mauro as a function of the total energy of the system through Applied and Computational Math and Stats the breakdown of normally hyperbolic invariant manifold University of Notre Dame located around the saddle. [email protected] Tamiki Komatsuzaki Samuel A. Isaacson Hokkaido University Boston University [email protected] Department of Mathematics and Statistics [email protected] Mikito Toda Nara Women’s University [email protected] MS94 Uniform Asymptotic Approximation of Diffusion to Hiroshi Teramoto aSmallTarget Hokkaido University [email protected] The problem of the time required for a diffusing molecule within a large bounded domain to first locate a small tar- get is prevalent in biological modeling. I consider this MS95 problem for a small spherical target. Uniform in time Control of a Model of DNA Opening Dynamics via asymptotic expansions in the target radius of the solu- Resonance with a Terahertz Field tion to the corresponding diffusion equation is developed. The approach is based on combining short-time expansions We study the internal resonance, energy transfer, and con- using pseudo-potential approximations with long-time ex- trol of DNA opening dynamics via parametric resonance. pansions based on first eigenvalue and eigenfunction ap- The model is a chain of pendula in Morse potential that proximations. These expansions allow the calculation of takes into account helicity, inhomogeneity, and environ- DS15 Abstracts 185

mental effects. While the model is robust to noise, we bility patterns for such breather solutions. demonstrate the possibility of triggering its opening dy- namics by targeting certain internal modes with specific Itay Grinberg terahertz fields. This may suggests that DNA natural dy- Faculty of Mechanical Engineering namics can be significantly affected by terahertz radiation Technion - Israel Institute of Technology exposures. [email protected]

Wang-Sang Koon Oleg Gendelman California Institute of Technology Technion Israel Institute of Technology [email protected] [email protected]

MS95 MS96 Obtaining Coarse-Grained Models from Multiscale Stable Two-Dimensional Solitons in Free Space: Data Gross-Pitaevskii Equations with the Spin-Orbit Coupling In many applications it is desirable to infer stochastic coarse-grained models from observational data of a multi- Abstract not available. scale process. Estimators such as the maximum likelihood estimator can, however, be strongly biased in this setting. Boris Malomed In this talk we discuss a novel inference methodology that Department of Physical Electronics, Faculty of Engr. does not suffer from this drawback. Moreover, we exem- Tel Aviv University, 69978 ISRAEL plify through a real-world data set how these data-driven [email protected] coarse-graining techniques can be used to study the statis- tical properties of a given temporal process. MS96 Sebastian Krumscheid Nonlinear Dynamics of Non-Stretched Membrane Ecole´ Polytechnique F´ed´erale de Lausanne (EPFL) sebastian.krumscheid@epfl.ch We present the analytical study of resonance non- stationary dynamics in the discrete initially non-stretched Greg Pavliotis membrane. The model consists of the weightless string Imperial College London withnattachedmasseswhicharesupportedinturnbyn [email protected] orthogonal weightless strings. It is shown that the intense energy exchange(nonlinear beats) in such discrete mem- Serafim Kalliadasis brane can be realized between different parts of the sys- Department of Chemical Engineering tem (effective particles). Its analytical description is ob- Imperial College London tained in terms of limiting phase trajectories (LPT) with [email protected] using the non-smooth transformations. The LPT bounds the domain of ordered motion in the phase space of the system. Increase of the excitation energy leads to two dy- MS95 namical transitions caused by instability of one of nonlin- Mode-Specific Effects in Structural Transitions of ear normal modes and LPT, respectively. As a result of Atomic Clusters with Multiple Channels the second transition the non-stationary energy localiza- tion arises. The obtained analytical solutions are confirmed We present the dynamical origin of mode-specific effects by numerical simulations. in structural transitions of atomic clusters with multiple channels. We employ the hyperspherical coordinates to Leonid Manevich identify reactive modes and driving modes for the respec- Semenov Institute of Chemical Physics tive channels of structural transitions. It is shown that Russian Academy of Sciences the branching ratios among different channels depend sig- [email protected] nificantly on the modes that are initially activated. Such mode-specific branching ratios are explained in terms of the dynamical coupling and energy transfer between reactive MS96 modes and driving modes. Mixed Solitary Shear Waves in a Granular Net- work Tomohiro Yanao Waseda University We study primary pulse transmission in two-dimensional [email protected] granular networks and predict a new type of mixed nonlin- ear solitary pulses shear waves, and pulse equi-partition between the chains of the network. An analytical model is MS96 asymptotically studied, based on the one-dimensional non- Discrete Breathers in Vibro-Impact Lattice Models linear mapping technique of Starosvetsky. To confirm the theoretical predictions we experimentally tested a series of Vibro-impact models offer a unique opportunity for ob- two-dimensional granular networks, and validated the oc- taining exact analytic solutions for discrete breathers in currence of strong energy exchanges and equi-partition for one-dimensional and two-dimensional systems (with triv- sufficiently large number of beads. ial possibility of generalization for 3D case). The solutions are obtained both for Hamiltonian models and for their Yijing Zhang forced/damped counterparts. Moreover, a formalism based University of Illinois at Urbana-Champaign on saltation matrices allows efficient analysis of global sta- [email protected] 186 DS15 Abstracts

Md. Arif Hasan Science Foundation (grant No. 2008122) is acknowledged. Mechanical Science and Engineering University of Illinois [email protected] Alexander Nepomnyashchy Department of Mathematics Yuli Starosvetsky Technion Technion, Israel Institute of Technology [email protected] [email protected] Vladimir A. Volpert D. Michael McFarland, Alexander Vakakis Northwestern University University of Illinois [email protected] [email protected], [email protected] Yulia Kanevsky Technion - Israel Institute of Technology MS97 [email protected] Cyclic Drug Delivery Devices and Monotone Dy- namical Systems MS97 In the case of a gel membrane geometry, we show existence Fluid Flow and Drug Delivery in a Brain Tumor of oscillatory solutions corresponding to the system oscil- lating between the collapsed and the swollen phases, as the We consider the problem of steady/unsteady fluid flow and ionic concentration reaches a critical threshold. We apply drug delivery in a growing brain tumor. Objective is to the theory to the design of a cyclic drug delivery device ac- understand the physiology of fluid flow and examine the tivated by a chemical reaction that releases the positively effect of concurrent application of two anti-cancer drugs charged ions that trigger the volume transition. in a brain tumor. Therapeutic Index, which is a measure of efficiency of drug delivery in the tumor, is determined Maria-Carme Calderer for different values of the parameters and discussed in the Deparment of Mathematics absence or presence of drugs’ interactions. University of Minnesota, USA [email protected] Ranadhir Roy University of Texas-Pan American [email protected] MS97 Evaluation of the Diffusion Coefficient of Nanopar- Daniel Riahi ticles Using Mathematical Simulation University of Texas - Pan American [email protected] We developed a novel, non-expensive nanoparticle (NP) drug-carrying system produced by self-assembly. A major objective was to evaluate the NP diffusion properties. To MS98 characterize their drug-release properties drug-loaded par- HIV Viral Rebound Times Following Suspension of ticles were placed in the donor of a double-compartment Art: Stochastic Model Predictions diffusion cell and the drug concentration in the receiver was sampled periodically. In this study we show a mech- Suspension of antiretroviral treatment (ART) for HIV typ- anistic model and mathematical simulation that, coupled ically leads to rapid viral load rebound to pre-treatment with the experimental results, was used to evaluate the levels. However, reports suggest that early ART initiation nanoparticle diffusion coefficient. may delay viral rebound, for months, years, or permanently (post-treatment control, PTC), after ART suspension. We Giora Enden present a model of post-treatment HIV dynamics. From Department of Biomedical Engineering, Ben-Gurion a branching process formulation we derive viral rebound University time probability densities and the probability of PTC. Us- Israel ing these, we discuss viral rebound times and conditions [email protected] for PTC.

Amnon Sintov Jessica M. Conway Department of Biomedical Engineering, Ben-Gurion Pennsylvania State University University [email protected] [email protected] MS98 MS97 Modeling HCV Infection: Viral Dynamics and Viscoelastic Effects in Drug Delivery Genotypic Diversity

Classical models of Hookean solid and Newtonian liquid Hepatitis C virus (HCV) is present in the host with multi- may be insufficient for description of biological fluids and ple variants generated by its error prone RNA-dependent materials used in controlled drug delivery. Instead, differ- RNA polymerase. We developed a series of models of viral ent viscoelastic models may be appropriate. We present a dynamics for non-overlapping generations, based on differ- number of examples where viscoelasticity effects are signifi- ence equations, that allows us to follow the diversification cant. Among them are: (i) non-Fickian drug release from a of HCV virus early on during infection. We compared the swelling polymer particle; (ii) dynamics of a pore in a lipid analytical solutions of these models with a more detailed membrane; (iii) drug delivery through a mucus layer in pul- agent-based model of the HCV lifecycle. We found that monary airways. The support of the US-Israel Binational the simplified model describes infection well, as long as DS15 Abstracts 187

saturation effects are not present. We then compared the such a relation. predictions of these models with data from acute infection in 9 plasma donors, with frequent sampling early in infec- Kimberley Jones tion. School of Mathematical & Statistical Sciences Arizona State University, Tempe, AZ, 85287 Ruy M. Ribeiro [email protected] Theoretical Biology and Biophysics Los Alamos National Laboratory Wenbo Tang [email protected] Arizona State University [email protected]

MS98 Modeling Equine Infectious Anemia Virus Infec- MS99 tion: Virus Dynamics, Immune Control, and Es- Flow and Grow: Experimental Studies of Time- cape Dependent Reaction-Diffusion-Advection Systems

Equine Infectious Anemia Virus is a retrovirus that estab- When a reaction-diffusion-advection system becomes non- lishes persistent infection in horses. Mathematical mod- autonomous, a new dimensionless parameter emerges: γ, els of within-host infection dynamics including immune re- the ratio of growth to flow timescales. For γ ∼ 1, the in- sponses will be presented. Analysis of the models yields teraction between growth and flow can produce complex thresholds that would be necessary for immune responses resonance phenomena. My team and I have developed an to successfully control infection. Furthermore, model re- experimental apparatus capable of simultaneous measure- sults predict the conditions under which multiple compet- ments of velocity fields and front locations in RDA. I will ing strains coexist or a subdominant viral strain escapes present studies varying γ = 1 and discuss implications for antibody neutralization and dominates the infection. Nu- phytoplankton growth in Earth’s oceans, where γ =0.8. merical simulations are presented to illustrate the results. Douglas H. Kelley University of Rochester Elissa Schwartz 218 Hopeman Engineering Building Rochester, NY Washington State University 14627-0132 [email protected] [email protected]

MS98 MS99 Modeling HIV Infection Dynamics under Condi- Lagrangian Coherent Structures for Reaction tions of Drugs of Abuse Fronts in Unsteady Flows

Drugs of abuse are associated with higher viral loads and Recent theoretical and experimental investigations have lower host-immune responses in HIV-infected drug abusers. highlighted the role of invariant manifolds, termed burn- To explore effects of drugs of abuse on HIV infection, I will ing invariant manifolds (BIMs), as one-way barriers to present dynamical system models that agree well with ex- reaction fronts propagating through time-independent or perimental data from simian immunodeficiency virus infec- time-periodic flows. This talk extends the concept of BIMs tions of morphine-addicted macaques. Using our models, to unsteady flows, thereby constructing coherent struc- we evaluate morphine-induced alterations in target cell sus- tures that organize and constrain the propagation of re- ceptibility and HIV-specific immune response that result in action fronts through general flows. Following Farazmand, higher viral replications and accelerated disease progres- Blazevski, and Haller [Physica D 278279, 44 (2014)], we sions. characterize coherent structures as curves of minimal La- grangian shear. Naveen K. Vaidya Dept of Maths & Stats, University of Missouri - Kansas Kevin A. Mitchell City University of California, Merced Kansas City, Missouri, USA Physics [email protected] [email protected]

John R. Mahoney MS99 University of California, Merced The Domain Dependence of Chemotaxis in a Two- [email protected] Dimensional Turbulent Flow

Coherent structures are ubiquitous in environmental and MS99 geophysical flows. Recent advances in the identification of Transport in Chaotic Fluid Convection finite-time transport barriers have enabled the extraction of organizing templates for passive scalars in the limit of Many interesting problems can be formulated as a diffusing infinitesimal diffusion. In this presentation, we try to re- concentration field that is also advected by a complex fluid late Lagrangian mixing and its corresponding measures to flow in a large spatially-extended domain. We explore the reaction processes in turbulent flows. Using a specific ex- case where this field is also reacting, as in chemical and ample of chemotaxis process in turbulence, we demonstrate combustion problems, or motile, as in bioconvection. Us- that elliptic regions of the flow trigger higher uptake ad- ing large-scale parallel numerical simulations we quantify vantage for motile species of microorganisms. We analyze the dynamics of a propagating front in a chaotic flow field how the flow field and the relevant flow topology lead to and the complex patterns of bioconvection for conditions 188 DS15 Abstracts

accessible to experiment. mike.jeff[email protected]

Mark Paul Department of Mechanical Engineering MS100 Virginia Tech Grazing Bifurcations in Engineering and Medical [email protected] Systems

Abstract not available. MS100 Some Nonsmooth Problems Inspired by Concep- Marian Wiercigroch tual Climate Models University of Aberdeen King’s College In this talk, I’ll outline the development of a global en- [email protected] ergy balance model that includes ice-albedo feedback and greenhouse gas effects. I’ll explore how the choice of temperature-dependent albedo affects transitions between MS101 stable steady states and periodic orbits of the system by Nonlinear Dynamics of Variational Data Assimila- applying modern techniques from nonsmooth dynamical tion systems. Using the path integral formulation of statistical data as- Anna M. Barry similation, we show how to find the consistent global min- Institute for Mathematics and its Applications imum path, show its dependence on the number of mea- University of Minnesota surements at each observation time, and demonstrate that [email protected] in certain parameter regimes, the corrections to the varia- tional approximation is small and computable. MS100 Henry D. Abarbanel Continuation of Chatter in a Mechanical Valve Physics Depratment Univ of California, San Diego This presentation considers the analysis of periodic chat- [email protected] ter in a mechanical pressure-relief valve, with emphasis on global interactions associated with a Shilnikov bifurca- Kadakia Nirag tion. It reviews work in non-smooth systems by Piiroinen UCSD and Nordmark for the numerical parameter continuation [email protected] of periodic orbits with infinitely many switches in finite time, using forward integration and nonlinear root solvers, and describes an alternative formulation expressed in terms Jingxin Ye of coupled boundary-value problems, implemented in the Department of Physics COCO framework. University of California at San Diego [email protected] Harry Dankowicz University of Illinois at Urbana-Champaign Uriel I. Morone, Daniel Rey Department of Mechanical Science and Engineering UCSD [email protected] [email protected], [email protected]

Erika Fotsch University of Illinois at Urbana-Champaign MS101 [email protected] Attractor Comparisons Based on Density

Alan R. Champneys In this work a chaotic attractor is described as a density University of Bristol distribution in phase space. Describing the attractor as [email protected] a density allows attractors to be compared using a small number of coefficients. Fits of these comparison coefficients as a function of some parameter change in the attractor MS100 can be used to predict how the attractor will change as a Lost in Transition: Nonlinearities in the Dynamics parameter changes. These density comparisons are used of Switching here to detect nonlinearity in a simple electronic circuit or to track parameter changes in a circuit based on the Rossler When a system transitions abruptly from one behaviour system. Comparisons between attractors could be useful to another, empirical models often describe well what hap- for tracking changes in an experiment when the underlying pens just after and just before the transition, but not dur- equations are too complicated for vector field modeling. ing. Worse, attempts to model the switch itself may in- volve complex higher dimensional and smaller scale pro- Thomas L. Carroll cesses. We can access the hidden dynamics of the transi- Naval Reseach Laboratory tion, though, using simple dynamical principles. To do so [email protected] fully requires a nonlinear theory of transitions in piecewise smooth dynamical systems. MS101 Mike R. Jeffrey Manifold Learning Approach for Modelling Col- University of Bristol lective Chaos in High-Dimensional Dynamical Sys- DS15 Abstracts 189

tems reside.

It has been known that a certain dynamical system exhibits James Bagrow lower-dimensional motion at a macroscopic level whereas Department of Mathematics & Statistics it also keeps high-dimensional chaos at a microscopic level, University of Vermont called collective chaos. In this study, we propose an ap- [email protected] proach based on manifold learning in order to extract vari- ables constructing nonlinear coordinate to the attractor of collective chaos. We apply the proposed approach to mod- els including sparse networks of chaotic maps and leaky MS102 integrate-and-fire neurons. A Network Measure for the Analysis and Visual- ization of Large-Scale Graphs Hiromichi Suetani Department of Physics and Astronomy Kagoshima University Given an undirected graph, we describe a two-dimensional [email protected] integer-valued measure, the Q-matrix, based on the con- nected component size distribution of its degree-limited subgraphs. This generalization of the degree distribution MS101 yields a small sparse matrix representing the number of Precision Variational Approximations in Statistical weakly connected components of a particular size during Data Assimilation a prescribed percolation process. When viewed as a two- dimensional histogram, this landscape yields a canonic vi- Data assimilation (DA) comprises transferring information sual representation, i.e. an identification portrait, revealing from observations of a complex system to physically-based important network properties. system models with state variables x(t). Typically, the ob- servations are noisy, the model has errors, and the initial Roldan Pozo state of the model is uncertain, so the DA is statistical. National Institute of Standards and Technology, USA One can thus ask questions about expected values of func- [email protected] tions G(X) on the model path X = {x(t0),...,x(tm)} as it moves through an observation window {t0,...,tm}.The probability distribution on the path P (X)=exp[−A0(X)] MS102 determines these expected values. Variational methods seeking extrema of the ‘action’ A0(X) are widespread for Revealing Collectivity in Evolving Networks: A estimating G(X) in many fields of science. In a path Random Matrix Theory Approach integral formulation of statistical DA, we consider vari- ational approximations in a standard realization of the Networks are the result of the tangled interconnections action where measurement and model errors are Gaus- among their nodes. As the network evolves, group of nodes sian. We (i) discuss an annealing method for locating the often undergo similar evolution patterns, giving rise to col- path X0 giving a consistent global minimum of the ac- 0 lective behavior. Here, we aim to uncover and quantify the tion A0(X ), (ii) consider the explicit role of the number degree of collectivity in the evolution of a complex network. of measurements at each measurement time in determin- 0 In particular, we use Random Matrix Theory to identify ing A0(X ), and (iii) identify a parameter regime for the significant correlations between the temporal topological scale of model errors which allows X0 to give a precise 0 properties (e.g. degree, centrality) of nodes. We apply our estimate of G(X ) with computable, small higher order method to both functional networks, obtained from stocks corrections. and climate correlation data, and structural networks, ob- tained from Internet AS-level connectivity data. Jingxin Ye Department of Physics University of California at San Diego Saray Shai [email protected] Department of Mathematics University of North Carolina at Chapel Hill [email protected] MS102 Shadow Networks: Discovering Hidden Nodes with Models of Information Flow MS103 On the Computation of Attractors for Delay Dif- Complex, dynamic networks underlie many systems, and ferential Equations understanding these networks is the concern of a great span of important scientific and engineering problems. Quanti- tative description is crucial for this understanding yet, due In this talk we will introduce a numerical method which to a range of measurement problems, many real network allows to approximate (low dimensional) invariant sets for datasets are incomplete. Here we explore how accidentally infinite dimensional dynamical systems. We will particu- missing or deliberately hidden nodes may be detected in larly focus on the computation of attractors for delay dif- networks by the effect of their absence on predictions of the ferential equations. The numerical approach is inherently speed with which information flows through the network. set oriented - that is, the invariant sets are computed by a We use Symbolic Regression (SR) to learn models relating sequence of nested, increasingly refined approximations -, information flow to network topology. These models show and does not rely on long term simulations of the underly- localized, systematic, and non- random discrepancies when ing system. applied to test networks with intentionally masked nodes, demonstrating the ability to detect the presence of missing Michael Dellnitz nodes and where in the network those nodes are likely to University of Paderborn, Germany 190 DS15 Abstracts

[email protected] [email protected]

MS103 MS104 Computing Coherent Sets in Turbulent Systems Finite-Time Lagrangian Transport Through Sur- faces in Volume-Preserving Flows In time dependent dynamics, it is often possible to divide phase space into sets which are seperated by transport bar- We present a Lagrangian approach to the quantification of riers. Finding these sets helps to understand the global transport of conserved quantities through a given hyper- dynamical behavior of systems arising in, e.g. atmospheric surface in general time-dependent, n-dimensional volume- flows, plasma physics and biological models. In this talk preserving flows. This is of significant importance for (i) we present a new approach for the computation of coher- the calculation of coherent transport by Lagrangian mate- ent sets by incorporating time-continuous diffusion into the rial sets such as coherent vortices in geophysical fluid flows, model. This leads to an advection-diffusion equation (the and (ii) semi-Lagrangian approaches to numerically solving Fokker-Planck equation) whise solution we approximate scalar advection equations. using spectral collocation. The approach does not need Daniel Karrasch any particle trajectories and is therefore suited for systems ETH Zurich, Switzerland where these are hard to obtain, e.g. turbulent systems. [email protected] Andreas Denner Center for Mathematics MS104 Technische Universitaet Muenchen [email protected] A Direct Method for Computing Failure Bound- aries of Non-autonomous Systems

Oliver Junge We present an efficient method, based on continuation of a Center for Mathematics two-point boundary value problem, to investigate the pa- Technische Universitaet Muenchen, Germany rameter dependence of system behaviour for models that [email protected] are subject to an external forcing. As an example we con- sider a model of a post-tensioned self-centring frame that experiences an earthquake. The failure boundary is the MS103 boundary of the region in the space of possible earthquakes The Geometry of Lagrangian Coherent Structures for which the frame displacement remains within a given range. We propose a novel, geometric method to identify subsets of phase space that retain small boundary size relative Hinke M. Osinga to volume as they are evolved by a nonlinear dynamical University of Auckland system. We describe a computational method to identify Department of Mathematics coherent sets based on eigenfunctions of a new dynamic [email protected] Laplacian operator. Finally, we demonstrate that the dy- namic Laplacian operator can be realised as a zero-diffusion limit of the classical probabilistic method for finding coher- MS104 ent sets, which is based on small diffusion. Interactions Between Noise and Rate-Induced Tip- ping Gary Froyland UNSW Australia A non-autonomous system passes a tipping point when [email protected] gradual changes in input levels cause the output to change suddenly. I investigate a new way to help detect tipping before it occurs. For rate-induced tipping, analysing how MS103 much the system deviates from the quasi-steady state equi- librium gives an early-warning indicator. I show that early- Coherent Families: Spectral Theory for Transfer warning indicators are present as soon as the most likely Operators in Continuous Time path for escape deviates from the quasi-steady state.

The decomposition of the state space of a dynamical sys- Paul Ritchie tem into metastable or almost-invariant sets is important University of Exeter for understanding macroscopic behavior. This concept is Mathematics research Institute well understood for autonomous dynamical systems, and [email protected] has recently been generalized to non-autonomous systems via the notion of coherent sets. We elaborate here on the theory of coherent sets in continuous time for periodically- MS104 driven flows and describe a numerical method to find pe- Rate-Induced Bifurcations in Slow-Fast Systems riodic families of coherent sets without trajectory integra- tion. Rate-induced bifurcations describe the failure to track a moving stable state in systems with drifting parameters. Peter Koltai Unlike classical bifurcations, they occur only above some Free University Berlin critical drift rate. We investigate rate-induced bifurcations [email protected] in slow-fast systems, using the theory of folded singulari- ties and canards, to uncover thresholds with intricate band Gary Froyland structures, separating initial states that track the mov- UNSW Australia ing stable state from those that destabilise. These novel DS15 Abstracts 191

thresholds explain non-obvious tipping point and excitabil- Laboratoiredephysiqueth´eoriquedelamati`ere ity phenomena that often puzzle scientists. condens´ee [email protected] Sebastian M. Wieczorek University of Exeter Mathematics Research Institute MS105 [email protected] Application of First-Passage Ideas to the Statistics of Lead Changes in Basketball

MS105 We investigate occurrences of lead changes in NBA basket- First Passage Time Problems for Stochastic Hybrid ball games. For evenly-matched teams, so that the score Systems difference can be modeled as unbiased diffusion, the proba- bility P(t) that a lead change occurs at time t in a game of We review recent work on the analysis of first-passage time length T is exactly soluble and surprisingly has maxima at problems in stochastic hybrid systems. A stochastic hybrid t=0 and t=T. We generalize to teams of unequal strengths system involves the coupling between a piecewise determin- and also provide a criterion for when a lead of a given size istic dynamical system and a time-homogeneous Markov is safe. chain on some discrete space. Examples include voltage- gated ion channels, intermittent transport by molecular Sidney Redner motors, and stochastic neural networks. We construct a Boston University path-integral representation of solutions to the underlying Physics Department master equation, and use this to derive a large deviation [email protected] principle for escape problems. We show that the result- ing Hamiltonian is given by the principle eigenvalue of a Aaron Clauset linear operator that depends on the transition rates of the University of Colorado at Boulder Markov chain and the nonlinear functions of the piecewise Computer Science deterministic system. [email protected] Paul C. Bressloff University of Utah Marina Kogan Department of Mathematics University of Colorado bressloff@math.utah.edu Computer Science [email protected]

MS105 MS106 Exploration and Trapping of Mortal Random Walkers Bifurcation Analysis of a Model for the El Ni˜no Southern Oscillation The calculation of first passage times has a long history, more recently extended to ”anomalous” walks (subdiffu- We consider a phenomenological model for the El Ni˜no sive or superdiffusive) in addition to those that lead to or- Southern Oscillation system in the form of a delay- dinary diffusion. However, the possible death of a walker differential-equation. We conduct a bifurcation analysis before reaching its target has only recently been consid- of the model in the two parameters of seasonal forcing ered. Evanescence obviously profoundly affects quantities strength and oceanic wave delay time, dividing the param- such as the survival probability of a target. I will talk about eter plane into regions of different solution types. Our anal- the effects of evanescence on first passage properties. ysis highlights parameter sensitivity, explains and expands on previously published results and uncovers surprisingly Katja Lindenberg complicated behaviour concerning the interplay between Department of Chemistry and Biochemistry seasonal forcing and delay-induced dynamics. University of California San Diego, USA [email protected] Andrew Keane Department of Mathematics The University of Auckland Santos B. Yuste, Enrique Abad [email protected] Universidad de Extremadura [email protected], eabad@unex es Bernd Krauskopf University of Auckland MS105 Department of Mathematics Trajectory-to-Trajectory Fluctuations in the First- [email protected] Passage Phenomena in Bounded Domains Claire Postlethwaite We propose a novel method to quantify the trajectory-to- University of Auckland trajectory fluctuations of the first passage of a Brownian [email protected] motion (BM) to targets on the boundary of compact do- mains, based on the distribution of the uniformity index, measuring the similarity of the first passage times of two MS106 independent BMs starting at the same location. This anal- Interplay of Adaptive Topology and Time Delay in ysis permits us to draw several general conclusions about the Control of Cluster Synchronization the importance of the trajectory-to-trajectory fluctuations on the first-passage behavior. We suggest an adaptive control scheme for the control of zero-lag and cluster synchronization in delay-coupled net- Gleb Oshanin works. Based on the speed gradient method, our scheme 192 DS15 Abstracts

adapts the topology of a network such that the target state semiconductor laser with two delayed optical feedbacks. is realized. The emerging topology is characterized by a delicate interplay of excitatory and inhibitory links leading Serhiy Yanchuk to the stabilization of the desired cluster state. As a cru- Humboldt University of Berlin cial parameter determining this interplay we identify the [email protected] delay time. Furthermore, we show how to construct net- works such that they exhibit not only a given cluster state but also with a given frequency. We apply our method to MS107 coupled Stuart-Landau oscillators, a paradigmatic normal Voltage Stability in Power Networks and Micro- form that naturally arises in an expansion of systems close grids to a Hopf bifurcation. The successful and robust control of this generic model opens up possible applications in a wide The AC power flow equations in a complex network display range of systems in physics, chemistry, technology, and life a rich phenomenology, but despite more than four decades science. of investigation the solution space remains poorly under- stood. Here we present a sharp and intuitive parametric Judith Lehnert condition for the existence of a stable power flow solution. Institut f¨ur Theoretische Physik Our condition immediately leads to non-conservative load- Technische Universit¨at Berlin ing margins, grid stability indices, and an accurate series [email protected] expansion of the stable solution. We illustrate our results with monitoring and control applications.

Alexander Fradkov Florian Dorfler Department of Theoretical Cybernetics Mechanical Engineering Saint-Petersburg State University University of California at Santa Barbara [email protected] dorfl[email protected]

Eckehard Sch¨oll, Philipp H¨ovel John Simpson-Porco Institut f¨ur Theoretische Physik University of California Technische Universit¨at Berlin [email protected] [email protected], [email protected] Francesco Bullo Anton Selivanov Mechanical & Environmental Engineering Department of Theoretical Cybernetics University of California at Santa Barbara Saint-Petersburg State University [email protected] [email protected]

MS107 MS106 Finding Useful Statistical Indicators of Instability Connection Between Extended Time-Delayed in Stochastically Forced Power Systems Feedback and Nonlinear Fixed-Point Problems Via a case study of a multi-machine power system, we iden- Time-delayed feedback control is an elegant method to find tify those (relatively few) system variables whose measured periodic orbits in an experiment without a-priori knowl- autocorrelation and variance provide reliable warning of in- edge of their shape. However, the method has various stability sufficiently before a collapse occurs. Our search topological restrictions, limiting the cases where it can be for such useful early warning signs (EWS) is enabled by a used. This presentation will use a singular perturbation semi-analytical calculation based on the Lyapunov equa- argument to show that for the extended time-delayed con- tion and is confirmed by simulations. We also study how trol (as introduced by Socolar) the classical odd-number these statistics are impacted by measurement noise and limitation still holds in the limit of slow updating of the discuss methods to reduce that impact. Several numerical reference signal. experiments confirm the validity of the identified EWSs and also reveal potential limitations.

Jan Sieber Goodarz Ghanavati, Paul Hines University of Exeter University of Vermont [email protected] [email protected], [email protected]

MS106 Taras Lakoba University of Vermont Pattern Formation in Systems with Multiple De- Department of Mathematics and Statistics layed Feedbacks [email protected]

Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding MS107 complicated oscillatory instabilities. We consider systems A Parametric Investigation of Rotor Angle Stabil- with multiple, hierarchically long time delays, and using a ity Using Direct Methods suitable space-time representation we uncover features oth- erwise hidden in their temporal dynamics. The behavior in An estimate of the critical clearing time (CCT) for a fault is the case of two delays is shown to ’encode’ two-dimensional formulated using the direct methods for power system tran- spiral defects and defects turbulence. A multiple scale anal- sient stability. By perturbing the energy functions used in ysis sets the equivalence to a complex Ginzburg-Landau the direct methods we present an analytic stability metric equation. We also demonstrate this phenomenon for a that can be used as a lower bound for the CCT. This new DS15 Abstracts 193

metric is used to support a parametric enquiry into the [email protected], stability of a small but non-trivial power system. [email protected], [email protected]

Lewis G. Roberts University of Bristol (UK) MS108 [email protected] A Global Bifurcation of Mixed-mode Oscillations

Alan R. Champneys This talk describes the existence of an elusive Shilnikov bi- University of Bristol furcation in the Koper model. This result closes a chapter [email protected] in one of the early and influential investigations of com- plex and chaotic mixed-mode oscillations. The bifurcation Mario Di Bernardo is located using a mixture of investigations of invariant University of Bristol manifold intersections and continuation methods. We also Dept of Engineering Mathematic study structural stability and global returns, leading us to [email protected] formulate a modified geometric model for a Shilnikov bi- furcationintheslow-fastregime.

Keith Bell Ian M. Lizarraga University of Strathclyde Cornell Center for Applied Mathematics Glasgow, Scotland [email protected] [email protected] John Guckenheimer MS107 Cornell University [email protected] Synchronization Stability of Lossy and Uncertain Power Grids Direct energy methods have been extensively developed for MS108 the transient stability analysis and contingency screening of Parameterization Method for Local Sta- power grids. However, there are no analytical energy func- ble/unstable Manifolds of Periodic Orbits tions proposed for power grids with losses. The difficulty originates from the nonlinear and asymmetric couplings I will discuss a numerical method for computing sta- among generators, which make the natural energy function ble/unstable manifolds of periodic orbits for differential nondecreasing. This paper extends the recently introduced equations that leads to high order Fourier-Taylor expan- Lyapunov Functions Family method to certify the synchro- sions for the invariant manifolds. The inputs are Fourier nization stability for lossy multimachine power grids. We series approximations of the periodic orbit and its Floquet present techniques to explicitly construct Lyapunov func- normal form which are computed using iterative algorithms tions and propose algorithms for Lyapunov function adap- and Galerkin projections. The Fourier approximation of tation to specific initial states, both by solving a number the Floquet normal form is then used in order to efficiently of linear matrix inequalities (LMIs). The Lyapunov Func- compute the parameterization of the local invariant mani- tions Family approach is also applicable to uncertain power fold. grids where the stable equilibrium is unknown due to possi- Jason Mireles James ble uncertainties in the mechanical torques. We formulate Rutgers University this new control problem and introduce techniques to cer- [email protected] tify the robust stability of a given initial state with respect to a set of equilibria. MS108 Konstantin Turitsyn Massachusetts Institute of Technology Practical Stability Versus Diffusion in the Spatial [email protected] Restricted Three-body Problem We examine the role of the four-dimensional centre man- Thanh Long Vu c ifold WL3 of the equilibrium L3 of the Spatial Restricted MIT Three-Body Problem, and its stable and unstable invari- [email protected] ant manifolds, in two dynamical processes for a small mass parameter. The first one consists of the Arnold diffusion MS108 mechanism associated to the existence of transition chains of heteroclinic connections. The second process consists of Bifurcations of Generalised Julia Sets Near the long-term confinement of trajectories in a practical stabil- Complex Quadratic Family ity domain in a large vicinity of L4,5.

We consider a nonanalytic perturbation of the complex Maisa O. Terra quadratic family that is associated to wild Lorenz-like ITA - Technological Institute of Aeronautics chaos. The perturbation opens up the critical value to Mathematics Department a disk and saddle points and their stable and unstable sets [email protected] appear. These sets interact with the generalised Julia set, leading to the (dis)appearance of chaotic attractors and to generalised Julia sets in the form of Cantor bouquets, Carles Sim´o Cantor tangles and Cantor cheeses. University of Barcelona [email protected] Stefanie Hittmeyer, Bernd Krauskopf, Hinke M. Osinga University of Auckland Priscilla de Sousa-Silva Department of Mathematics Instituto Tecnol´ogico de Aeron´autica, Brazil 194 DS15 Abstracts

[email protected] Sabato Santaniello University of Colorado [email protected] MS109 Perspectives on Theories of Diabetogenesis and Glucose Management MS109 Unification of Neuronal Spikes, Seizures, and The personalization of treatment is a key difficulty in the Spreading Depression clinical management of type 2 diabetes today. Although it is widely agreed that glucose control is central to anti- The pathological phenomena of seizures and spreading de- diabetic therapy, there is little consensus on how to achieve pression have long been considered separate physiological it. We believe that the concurrent measurement of redox events in the brain. By incorporating conservation of par- status, such as through glutathione in particular, can be ticles and charge, and accounting for the energy required to used to assess the progress of therapy as well as provide restore ionic gradients, we extend the classic HodgkinHux- quantitative targets for glucose control. In my talk I will ley formalism to uncover a unification of neuronal mem- describe reasons in support of this argument, and a mini- brane dynamics. By examining the dynamics as a function mal model for achieving it. I will also present a theory of of potassium and oxygen, we now account for a wide range diabetogenesis that implicates oxidative stress as a central of neuronal activities, from spikes to seizures, spreading causal factor, and our attempts at modeling it. depression (whether high potassium or hypoxia induced), mixed seizure and spreading depression states, and the Pranay Goel terminal anoxic wave of death. Such a unified framework Indian Institute for Science Education and Research demonstrates that all of these dynamics lie along a con- [email protected] tinuum of the repertoire of the neuron membrane. Our results demonstrate that unified frameworks for neuronal Saroj Ghaskadbi dynamics are feasible, can be achieved using existing bio- Dept. of Zoology logical structures and universal physical conservation prin- Savitribai Phule Pune University ciples, and may be of substantial importance in enabling [email protected] our understanding of brain activity and in the control of pathological states.

MS109 Steven J. Schiff Penn State University Therapeutic Mechanisms of High Frequency Center for Neural Engineering DBS in Parkinsons Disease: Neural Restoration sschiff@psu.edu Through Loop-Based Reinforcement

High frequency deep brain stimulation (HFS) is clinically Yina Wei recognized to treat parkinsonian movement disorders but Univ California Riverside its mechanisms remain elusive. Current hypotheses sug- [email protected] gest that the therapeutic merit of HFS stems from increas- ing the regularity of the firing patterns in the basal gan- Ghanim Ullah glia (BG). Although this is consistent with experiments University of South Florida in humans and animal models of Parkinsonism, it is un- [email protected] clear how the pattern regularization would originate from HFS. To address this question, we built a computational model of the cortico-BG-thalamo-cortical loop in normal MS109 and parkinsonian conditions. We simulated the effects Termination of Cardiac Alternans Using Isostable of subthalamic deep brain stimulation both proximally to Response Curves the stimulation site and distally through orthodromic and antidromic mechanisms for several stimulation frequencies Phase reduction has been tremendously useful for under- (20-180Hz) and, correspondingly, we studied the evolution standing the dynamics of nonlinear oscillators, but has of the firing patterns in the loop. The model closely repro- been difficult to extend to systems with stable fixed points, duced experimental evidence for each structure in the loop such as excitable systems. Using the notion of isostables, and showed that neither the proximal effects nor the dis- we present a general method for isostable reduction of ex- tal effects individually account for the observed pattern citable systems. This reduction is applied to both single- changes, while the combined impact of these effects in- and multi-cell systems of cardiac activity in order to for- creases with the stimulation frequency and becomes signifi- mulate an energy optimal control strategy to terminate cant for HFS. Perturbations evoked proximally and distally cardiac alternans, a precursor to cardiac arrest. propagate along the loop, rendezvous in the striatum, and, for HFS, positively overlap (reinforcement), thus causing Dan D. Wilson larger post-stimulus activation and more regular patterns Mechanical Engineering in striatum. Reinforcement is maximal for the clinically- University of California, Santa Barbara relevant 130Hz stimulation and restores a more normal ac- [email protected] tivity in the nuclei downstream. These results suggest that reinforcement may be pivotal to achieve pattern regular- Jeff Moehlis ization and restore the neural activity in the nuclei down- Dept. of Mechanical Engineering stream, and may stem from frequency-selective resonant University of California – Santa Barbara properties of the loop. [email protected]

Sridevi Sarma Johns Hopkins University MS110 [email protected] Triggers of Rogue Waves in Deep Water Envelope DS15 Abstracts 195

Equations case of inhomogeneous diffusion on a lattice. The minimal error on the macroscale is generally obtained by coupling Rogue ocean waves have caused considerable damage to patches with patch cores half as large as the patch, thus ships and coastal structures. We analyze the role of spa- creating coupling active over the other half of the patch. tial localization in triggering rogue waves in the modified The results indicate that patch dynamics is useful for com- nonlinear Schrodinger equation. Specifically, we develop a putational simulation of a wide range of systems with fine reduced order model that allows us to determine the char- scale roughness. acteristics of wave packets likely to focus and grow in am- plitude. We use this analysis to develop a computationally Anthony J. Roberts efficient scheme for predicting rogue waves by identifying University of Adelaide these potentially dangerous wave packets. [email protected]

Will Cousins MIT MS111 [email protected] Controlling Hyperbolic Trajectories and Invariant Manifolds in Flows Themistoklis Sapsis Massachusetts Institute of Techonology Hyperbolic trajectories are important in governing fluid [email protected] motion, since their attached stable and unstable manifolds form crucial flow separators. We derive the control veloc- ity ensuring that a hyperbolic trajectory follows specified n MS110 nonautonomous motion in IR . We control both the Lorenz Boundary Conditions and the Linking of Compu- system, and a 3D droplet model, respectively obtaining tational Domains in Patch Dynamics Schemes a specified long-term attractor, and intra-droplet mixing. Ongoing work on determining control velocities for obtain- Abstract not available. ing prescribed nonautonomous (un)stable manifold motion is also presented. I. G. Kevrekidis Princeton University Sanjeeva Balasuriya [email protected] University of Adelaide School of Mathematical Sciences [email protected] MS110 Resilient Algorithms for Reconstructing and Sim- Kathrin Padberg-Gehle ulating Gappy Flow Fields in CFD Institute of Scientific Computing TU Dresden It is anticipated that in future generations of massively [email protected] parallel computer systems a significant portion of proces- sors may suffer from hardware or software faults rendering large-scale computations useless. In this work we address MS111 this problem from the algorithmic side, proposing resilient Closed-Loop Control of Complex and Turbulent algorithms that can recover from such faults irrespective Flows Using Machine Learning Control: a Reverse of their fault origin. In particular, we set the foundations Engineering Approach of a new class of algorithms that will combine numerical approximations with machine learning methods. We propose a model-free methodology to find closed-loop control laws for complex and turbulent flows using genetic Seungjoon Lee programming. Avoiding the necessity to derive a model, Division of Applied Mathematics, Brown University the sensor-to-control law is derived by creating and evolv- seungjoon [email protected] ing expression-trees according to a cost function. We show the efficiency of the method by the control of strongly non- Ioannis Kevrekedis linear systems, and its practicality by exhibiting the results Princeton University obtained on four turbulent experimental flows. [email protected] Thomas Duriez Buenos Aires University George E. Karniadakis Laboratory of Fluid Dynamics Brown University [email protected] Division of Applied Mathematics george [email protected] Vladimir Parezanovic, Kai Von Krbek, Jean-Paul Bonnet, Laurent Cordier MS110 Institute PPRIME, CNRS [email protected], Better Buffers for Patches in Macroscale Simula- [email protected], tion of Systems with Microscale Randomness [email protected], The ‘equation-free’ methodology couples many small [email protected] patches of microscale computations across space to em- power computational simulation over macroscale spatial Bernd R. Noack domains of interest. We derive generally optimum cou- Institut PPRIME, CNRS pling of patches and core averaging when the microscale is [email protected] inherently ‘rough’ as in molecular or agent simulations. As a canonical problem in this universality class we analyse the Marc Segond, Markus W Abel 196 DS15 Abstracts

Ambrosys GmbH smoothly-patterned substrate, the fluid particle trajecto- [email protected], [email protected] ries are, to leading order in the layer thickness, geodesics on the two-dimensional curved space of the substrate. We use Nicolas Gautier, Jean-Luc Aider 3D-printed substrates to show that the pattern made by a PMMH Laboratory, UMR 7636 CNRS, ESPCI jet striking a bumpy surface is described by the geodesic [email protected], [email protected] equation. Because the geodesic equation is fourth order, the geodesics are chaotic even for simple substrates. This Cedric Raibaudo, Christophe Cuvier, Michel Stanislas could offer a new method of improving mixing by varying Laboratoire de M´ecanique de Lille, UMR CNRS 8107 the shape of the substrate. ´ Ecole Centrale de Lille Jean-Luc Thiffeault [email protected], [email protected], Dept. of Mathematics [email protected] University of Wisconsin - Madison [email protected] Antoine Debien, Nicolas Mazellier, Azeddine Kourta Labratoire PRISME, Universit´ed’Orl´eans, Orl´eans, Jay Johnson France University of Texas at Austin [email protected], [email protected] [email protected], [email protected] MS112 Steven Brunton Experimental Observation of Rhythm Control of University of Washington Human Gait Using Moving Floor [email protected] Human and animals maintain stability of gait and posture by tuning their motion rhythms. In order to approach this MS111 rhythm control mechanisms, human motion with floor dis- Mesohyperbolicity, Mix-Norm and the Hunt for turbance is measured and rhythm characteristic of human Mh370 is discussed. Response to high frequency floor disturbance during walking is observed for calculating the phase re- The disappearance of MH370 has exposed the disconcert- sponse curve, and response to rotational floor is measured ing lack of efficient methods for searching objects moving for considering the posture control. in a complex and dynamic environment. Lagrangian kine- matics of mesoscale features are visible in mesohyperbolic- Tetsuro Funato itymapswhichcanbeusedtopredictthetimeevolutionof Mechanical Engineering any initial distribution and incorporated in the design of a Japanese University of Electro-Communications search strategy. A modified version of DSMC search algo- [email protected] rithm determines multiple search agents trajectories using ergodicity ideas and the Mix-Norm as a metric. Shinya Aoi, Nozomi Tomita, Tsuchiya Kazuo Kyoto University Sophie Loire shinya [email protected], [email protected] University of California Santa Barbara u.ac.jp, [email protected] [email protected]

Hassan Arbabi MS112 UC Santa Barbara What Can Coupled, Nonlinear Oscillators Say [email protected] About Noisy, Perturbed Cockroaches

Stefan Ivic Cockroaches are remarkably stable runners, exhibiting Rijeka University rapid recovery from external perturbations. To uncover [email protected] the mechanisms responsible for this, we recorded leg kine- matics of freely running animals in both undisturbed and Patrick Clary perturbed trials. Perturbations were applied to single legs UCSB via magnetic impulses and the resulting transient effects [email protected] on all legs and recovery times to normal pre-perturbation kinematics were studied. We estimated coupling architec- tures and strengths by fitting data to a six leg-unit phase Bojan Crnkovic, Nelida Crnjaric-Zic oscillator model. Using maximum likelihood techniques, Rijeka University we found that a network with nearest-neighbor interleg [email protected], [email protected] coupling best fitted the data, and that, while coupling strengths vary among preparations, overall inputs enter- Igor Mezic ing each leg are approximately balanced and consistent. UCSB Simulations of models encountering perturbations suggest [email protected] that the coupling schemes estimated from our experiments allow animals relatively fast and uniform recoveries from perturbations. This is joint work with E. Couzin-Fuchs, T. MS111 Kiemel, O. Gal and A. Ayali. Control of Thin-Layer Flows with Patterned Sur- faces Philip Holmes Princeton University When a shallow layer of inviscid fluid flows over a Program in Applied and Computaional Mathematics & DS15 Abstracts 197

MAE Dept Department of Applied Mathematics [email protected] University of Colorado, Boulder [email protected]

MS112 Formation Mechanism for Basin of Attraction of MS113 Bipedal Working Models Statistical Physics Models for Critical Phenomena in Permafrost Lakes In this presentation, I will talk about the stability of simple bipedal walking models. Especially, I focus on the geomet- There is an interesting problem, where geometrical changes ric structure of basin of attraction. By some numerical of the patterns and its stochastic behavior can lead to the computations for the basin of attraction, interesting and critical phenomena in a climate system. As a result of tun- complex geometric structures, for example, the region is dra permafrost thawing, permafrost lakes have extended, thin and fractal-like, but the formation mechanism is not and methane from ground has entered the atmosphere. We known. I will explain the mechanism with the saddle prop- have suggested a nonlinear model for phase transitions in erty and hybridness of bipedal walking models. permafrost lakes (based on Ginzburg-Landau theory from statistical physics). We have applied this model to study Obayashi Ippei abrupt permafrost methane emission. Department of Matheamtics Kyoto University Ivan Sudakov [email protected] University of Utah Mathematics Department [email protected] MS112 Lateral Balance of Human Walking and Human Structure Interaction MS113 Growth and Fluctuations of Suncups on Alpine Although synchronisation of pedestrian frequencies to lat- Snowpacks: Comparison of Field Observations eral ground vibrations has been observed in the past, the with a Nonlinear Pde Model mechanism leading to this behaviour is still not well un- derstood. To this end experimental data from pedestrians A mathematical model for suncups on alpine snow exposed freely-walking on a laterally oscillating treadmill are anal- to solar radiation is compared with field observations. The ysed revealing adaptive stepping patterns. At the same model consists of a fourth order nonlinear partial differ- time simple spring-mass models of this motion are derived ential equation similar to the KPZ equation. The pat- and analysed. The applicability of Kuramoto synchronisa- terns fluctuate chaotically in time, and the fluctuations can tion model to capture this behaviour is examined. be described in terms of diffusion of individual suncups. The rate at which the suncups diffuse contains informa- John Macdonald tion about the effect of the suncups on the albedo of the Civil Engineering Department snow. University of Bristol [email protected] Tom Tiedje Faculty of Engineering Jeremy Burn University of Victoria University of Bristol [email protected] [email protected]¿ Kevin A. Mitchell Matteusz Bocian Simon Fraser University University of Exeter Department of Mathematics University of Bristol [email protected] [email protected]

Alan R. Champneys MS113 University of Bristol How Climate Model Complexity Impacts the Sta- [email protected] bility of the Sea Ice Cover Two types of idealized climate models find instabilities dur- MS113 ing the retreat of sea ice under global warming: (i) annual- The Evolution of Complexity in Arctic Melt Ponds: mean latitudinally-varying diffusive energy balance models a Statistical Physics Perspective and (ii) seasonally-varying single-column models. Compre- hensive global climate models, however, typically find no Recent analysis of Arctic melt pond images reveals that instabilities. To bridge this gap, we develop an idealized the pond shape transitions from simple to complex around model that includes both latitudinal and seasonal varia- a critical area of 100 square meters. To explain this on- tions. Our results suggest that the ice cover is significantly set of complexity, a two-dimensional Ising model for pond more stable than found in previous idealized models. evolution is proposed that incorporates ice-albedo feedback and the underlying thermodynamics. A second-order phase Till Wagner transition from isolated to clustered ponds is found, with Scripps Institution of Oceanography the pond complexity in the clustered phase consistent with University of California San Diego the observations. [email protected]

Yiping Ma Ian Eisenman 198 DS15 Abstracts

Scripps Institution of Oceanography of STN and GP populations (a ”micro-channel”) cannot [email protected] oscillate without self-excitation, in pairs they show rhyth- mic activity at a range of intrinsic frequencies, chosen dur- ing training. Adjusting the intrinsic frequency of a central MS114 channel selects groups of micro-channels via partial syn- Possible Mechanisms for Generation of Beta Oscil- chronisation. We describe the analysis and possible bio- lations in Parkinsons Disease logical interpretation of our model.

In Parkinson’s disease abnormal oscillations in neural ac- Roman M. Borisyuk tivity in beta frequency range (13-30Hz) have been ob- School of Computing and Mathematics, Plymouth served in the basal ganglia, and their power correlates with University the severity of symptoms. We consider a simple model of PL4 8AA, UK cortico-basal-ganglia circuit. We show that there exist dif- [email protected] ferent regions of its parameters for which the model can match the dataset of Tachibana et al. describing neural Robert Merrison-Hort activity in Parkinson’s disease. These different regions cor- Plymouth University respond to different mechanisms of oscillations’ generation. [email protected] Alexander Pavlides University of Oxford MS114 [email protected] Cortical Impact on the Dynamics of Subthalamo- pallidal Networks John Hogan Bristol Centre for Applied Nonlinear Mathematics Parkinsonian hypokinetic motor symptoms are associated Department of Engineering Mathematics, University of with the beta-band synchronized oscillations throughout Bristol basal ganglia-thalamo-cortical circuits. This study ex- [email protected] plores the oscillatory interactions between cortical and basal ganglia networks in Parkinson’s disease in the model Rafal Bogacz of the basal ganglia. The patterns of responses of beta- Associate Professor band bursting in the model suggest that the experimentally Oxford University, UK observed beta-band synchronization in Parkinson’s disease [email protected] may be promoted by the simultaneous action of both cor- tical and subthalamo-pallidal network mechanisms.

MS114 Leonid Rubchinsky Department of Mathematical Sciences Identifying and Tracking Transitions in Neural Indiana University Purdue University Indianapolis Spiking Dynamics in the Subthalamic Nucleus of [email protected] Parkinsons Patients

Accurate statistical modeling of spiking dynamics in neu- Sungwoo Ahn rological disease is important for understanding how the Indiana University Purdue University Indianapolis disease develops, progresses, and manifests clinical symp- [email protected] toms. In particular, abnormal oscillatory firing patterns of neurons in the subthalamic nucleus (STN) of patients with Elizabeth Zauber Parkinson’s disease (PD) have been postulated to play a Indiana University School of Medicine role in the pathogenesis of motor deficits. We present a [email protected] point process analysis framework that allows us to iden- tify and characterize the rhythmic dynamics in STN spike Robert Worth trains, test for statistically significant changes to those dy- Department of Neurosurgery namics, and track the temporal evolution of such changes. Indiana University School of Medicine The approach incorporates generalized linear modeling the- [email protected] ory for point processes with state space modeling to esti- mate, instant by instant, changes in the influence of past spiking history on the current spiking probability. We MS115 demonstrate the method on both simulated and actual data Topology Predicts Dynamics; Dynamics Constrain recorded from human STN. Topology Uri Eden Networks are often the structure on which high dimensional Associate Professor Department of Mathematics and dynamical systems operate. Inferring network topology Statistics from dynamics and constructing networks to exhibit tar- Boston University get dynamics are complimentary strategies to understand [email protected] their interplay. Recent efforts can infer the structure of a network from manipulations and observations of network dynamics. A computational study of a detailed model of a MS114 neuronal network suggests that networks with similar dy- Oscillations and Action Selection in a Multi- namics exist in connected sets in the space of all possible Channel Model of the Basal Ganglia networks. We present a population-level model of basal ganglia action Srinivas Gorur-Shandilya selection based on segregated oscillatory channels, star-like Interdepartmental Neuroscience Program connectivity and partial synchronisation. Although a pair Yale University, US DS15 Abstracts 199

[email protected] derstand and analyze data has led to an outburst of re- search into advanced methods of data based modeling. We address various approaches to network inference based on MS115 time series data. Data-Driven Network Inference: Achievements, Problems, Possible Research Directions Bj¨orn Schelter Institute for Complex Systems and Mathematical Biology Complex networks are powerful representations of spatially University of Aberdeen, UK extended systems and can advance our understanding of [email protected] their dynamics. A large number of analysis techniques is available that aim at inferring the underlying network Marco Thiel structure from data. Despite great successes in various Department of Physics - King’s College fields, there still exist a number of problems for which there University of Aberdeen, UK are currently no satisfactory solutions. This talk will dis- [email protected] cuss these problems as well as possible research directions to help find better solutions. MS116 Klaus Lehnertz Averaging and Kam Theory in Torus Canards Department of Epileptology University of Bonn, Germany We consider rotated slow-fast systems of van der Pol type. [email protected] Depending on the rotation speed, the resulting 3D system has 2 fast or 2 slow variables. There exists also an interme- diate region with three timescales. In the region of two fast MS115 variables we prove the existence of an invariant torus and Network Structure from Responses of Time- in the intermediate regime we use KAM theory to show the invariants existence of chaotic dynamics.

Inferring how complex systems are interconnected solely Albert Granados from dynamical experiments [1] constitutes a fundamental SISYPHE, INRIA inverse problem with practical relevance across the natural alberto.granados [email protected] and technical sciences. So far, most inference approaches either require a high degree of knowledge about the units and the coupling modes or rely on the system being in MS116 simple states such as close to fixed points. Moreover, most Averaging and Generic Torus Canards approaches require the knowledge of the temporal order of the units’ states or their relations. Here we present a com- Recently, torus canards have been identified in a range plementary approach that instead employs invariant mea- of neuronal burster models, and the majority of these sures (i.e. distributions of points sampled in state space) slow/fast systems have a single slow variable. The tran- in response to small driving forces. Given sufficiently long sition from spiking to bursting occurs via a torus canard time series, inference is successful for very distinct systems, explosion, resulting in the existence of non-generic torus from networks of chaotic oscillators to genetic regulatory canards within a small parameter range. We analyse a circuits underlying the circadian clock. These results ex- coupled neuron model with two slow variables, and using pand our ability to infer structural connectivity of networks averaging, identify folded saddle and node singularities. given temporally unordered observations, possibly stem- These structures and their bifurcations result in generic ming from different experiments with uncontrolled initial torus canards, leading to rich dynamics over a wide pa- conditions. [1] J. Phys. A: Math. Theor. 47:343001 (2014). rameter range.

Mor Nitzan Kerry-Lyn Roberts Hebrew University of Jerusalem University of Sydney Israel [email protected] [email protected]

Jose Casadiego MS116 Max Planck Institut for Dynamics and Self-Organization Torus Canard Breakdown [email protected] We discuss the conditions giving rise to torus and period- Marc Timme doubling bifurcation pathways from tonic spiking to burst- NetworkDynamics,MaxPlanckInst.f.Dyn.&Self-Org. ing in slow-fast systems typical in life science applications. Goettingen, Germany We employ Poincare return maps to disclose fine details of [email protected] the torus breakdown resulting in the rapid onset of sponta- neous bursting in a Hodgkin-Huxley type model of a hair cell. Hair cells are peripheral receptors serving on the first MS115 stage in transduction of mechanical stimuli to electrical Data Based Modelling: Inferring the Direct Di- signals in the senses of hearing and balance of vertebrates. rected Network Structure from Data These sensors rely on nonlinear active processes to achieve astounding sensitivity, selectivity and dynamical range. Recent years have seen a large increase in the availabil- ity of data. Increasing amounts of data play a key role Andrey Shilnikov in every aspect of our lives. Dealing with these data sets Neuroscience Institute and Department of Mathematics efficiently determines the success of projects, treatments, Georgia State University assessments, and analyses. This necessity to better un- [email protected] 200 DS15 Abstracts

Alexander Neiman tions. Probably, the most nontrivial situation is that of a Ohio University globally coupled populations, where one and the same force [email protected] acts on all oscillators in the ensemble. We give two exam- ples of chimera formation in such a setup, and describe the underlying mechanisms of sel-induced bistability between MS116 synchrony and asynchrony. The Interaction Between Classical Canards and Torus Canards Arkady Pikovsky Department of Physics Canards are separatrices of slow/fast systems that lie at the University of Potsdam, Germany intersection of attracting and repelling invariant slow man- [email protected] ifolds. Closely associated with folded equilibria, canards 3 have been studied extensively in R . Less well-understood Michael Rosenblum are torus canards, which lie at the intersection of attracting Potsdam University and repelling families of limit cycles. In this work, we ex- Department of Physics and Astronomy plore the relationship between folded node/saddle canards [email protected] and torus canards in various model systems.

Theodore Vo Azamat Yeldesbay University of Sydney Department of Physics and Astronomy [email protected] University of Potsdam, Germany [email protected]

MS117 MS117 The Kuramoto Model of Coupled Oscillators with a Bi-Harmonic Coupling Function” Maxim Komarov Mean Field Theory of Assortative Networks of Phase Oscillators We study synchronization in a Kuramoto model of glob- ally coupled phase oscillators with a bi-harmonic coupling In this talk I present a technique to study synchronization function, in the thermodynamic limit of large populations. in large networks of coupled oscillators, combining a mean We develop a method for an analytic solution of self- field approximation with the ansatz of Ott and Anton- consistent equations describing uniformly rotating complex sen. The formulation is illustrated on a network Kuramoto order parameters, both for single-branch (one possible state problem with degree assortativity and correlation between of locked oscillators) and multi-branch (two possible val- the node degrees and the natural oscillation frequencies. ues of locked phases) entrainment. We show that syn- We find that degree assortativity can induce transitions chronous states coexist with the neutrally linearly stable from a steady macroscopic state to a temporally oscillating asynchronous regime. The latter has a finite life time for macroscopic state through Hopf and SNIPER bifurcations. finite ensembles, this time grows with the ensemble size as apowerlaw. Juan G. Restrepo Maxim Komarov Department of Applied Mathematics Department of Physics and Astronomy University of Colorado at Boulder Potsdam University [email protected] [email protected] Edward Ott University of Maryland MS117 Inst. for Research in Electronics and Applied Physics On the Mechanical Origin of Chimera States [email protected]

Previously, we have demonstrated the emergence of chimera states in an experiment with mechanical oscilla- MS118 tors (Martens, E. A., et al. PNAS (2013)) and introduced Singular Bogdanov-Takens Bifurcations in the a mathemtical model based on mechanical principles. Here, Plane I analyze this model and establish a link to abstract math- ematical models in which chimera were originally discov- We present perturbations from planar vector fields having a ered. With the analysis, I explain the stability diagram, line of zeros and representing a singular limit of Bogdanov- discuss a new state and provide the first physical interpre- Takens (BT) bifurcations. We introduce the notion of tation of how chimeras may arise in real world situations. slow-fast BT-bifurcation and we provide an overview of a complete study of the bifurcation diagram and the related phase portraits, based on geometric singular perturbation Erik A. Martens theory, including blow-up. Max Planck Institute for Dynamics & Self-Organization [email protected] Peter De Maesschalck Hasselt University [email protected] MS117 Chimera States in Globally Coupled Oscillators MS118 Chimera states in coupled oscillator systems, where despite Canard Orbits in Planar Slow-Fast Piecewise- of full symmetry, part of the oscillators are synchronized Linear Systems while other are desynchronized, have attracted large inter- est recently, also because of several experimental realiza- The basis of most neuron models is to assume that a neu- DS15 Abstracts 201

ron behaves as an electrical circuit, which are faithfully Emilio Freire modeled by piecewise linear (PWL) systems. Also, neuron Departamento Matematica Aplicada II models are characterized by different time scales. In this Universidad de Sevilla, Spain work, we analyze the existence of canard orbits in a family [email protected] of planar PWL slow-fast systems. The purpose is to use the results to provide models of neurons equally efficient to the smooth models, offering better mathematical tractability. MS119 Symbolic Dynamical Unfolding of Spike-Adding Bi- Soledad Fernandez-Garcia furcations in Chaotic Neuron Models Inria Paris-Rocquencourt France We show the systematic changes in the topological struc- [email protected] ture of chaotic attractors occurring as spike-adding and ho- moclinic bifurcations are encountered in the slow-fast dy- Mathieu Desroches, Martin Krupa namics of neuron models (detailed in the Hindmarsh-Rose INRIA Paris-Rocquencourt model), where we show that the UPOs appearing after each [email protected], [email protected] spike-adding bifurcation are associated with specific sym- bolic sequences opened when the small parameter of the Antonio E. Teruel system decreases. This allows us to understand how these University of the Balearic Islands bifurcations modify the internal structure of the chaotic Palma, Spain attractors. [email protected] Roberto Barrio University of Zaragoza, SPAIN MS118 [email protected] Theoretical Analysis of Homoclinic Canards Marc Lefranc Abstract not available. PhLAM/Universit´e Lille I, France Jean-Pierre Francoise [email protected] University Pierre & Marie Curie - Paris 6 France M. Angeles Martinez [email protected] University of Zaragoza SPAIN [email protected] MS118 Folded Nodes, Canards and Mixed Mode Oscila- Sergio Serrano tions in 3D Piecewise-Linear Systems University of Zaragoza, SPAIN [email protected] New advances in 3D piecewise-linear slow-fast systems (PWL) are presented. In particular, a complete compari- son with the smooth case near folded singularities is shown: MS119 singular phase portraits, singular weak and strong canards Stokes Phenomenon in a Singularly Perturbed Dif- and control of the number of maximal canards are obtained ferential Equation in a way that is entirely compatible with the smooth case. Furthermore, by using previous analysis we present a mini- It is well known that bifurcation problems can often be mal model displaying periodic canard induced mixed mode studied with the help of singular perturbation theory. In oscillations near a PWL folded-node. these problems invariant manifolds and solutions can be found in the form of formal series. The series typically Antonio E. Teruel diverge and relations with analytical solutions is described University of the Balearic Islands by the Stokes phenomenon. In this talk we discuss the Palma, Spain recent developments of the theory and illustrate it with [email protected] examples.

Mathieu Desroches Vassili Gelfreich INRIA Paris-Rocquencourt University of Warwick, UK [email protected] [email protected]

Enrique Ponce Departamento de Matem´atica Aplicada MS119 EEscuela T´ecnica Superior de Ingeniera, Seville, Spain Canard Orbits and Mixed-Mode Oscillations in a [email protected] Chemical Reaction Model

Rafel Prohens To study how mixed-mode oscillations are organised in University of the Balearic Island, Palma Spain Koper’s three-dimensional chemical reaction model, we [email protected] compute the two-dimensional attracting and repelling slow manifolds and their intersection curves, known as canard Antoni Guillamon orbits. We also show how a tangency between the repelling Politecnic University of Catalunya slow manifold and the two-dimensional unstable manifold [email protected] of a saddle-focus equilibrium shapes the dynamics locally 202 DS15 Abstracts

and globally. Universitat Augsburg Germany Bernd Krauskopf, Jose Mujica, Hinke M. Osinga [email protected] University of Auckland Department of Mathematics [email protected], [email protected], MS120 [email protected] On the Complete Dynamical Behavior for Three Dimensional Stochastic Competitive Lotka- VolterraSystems MS119 Homoclinic Orbits With Many Loops Near a 02iω Abstract not available. Resonant Fixed Point Of Hamiltonian Systems Jifa Jiang In this talk we study the existence of homoclinic connec- Shanghai Normal University tions near the equilibrium point of a family of Hamiltonian [email protected] systems in the neighborhood of a 02iω resonance. For re- versible non Hamiltonian vector fields, the splitting of the homoclinic orbits lead to exponentially small terms which MS120 prevent the existence of homoclinic connections with one Self-similarity in Stochastic PDEs loop to periodic orbits of size smaller than an exponentially small critical size. The same phenomenon occurs here but This talk present some methods to study the self-similarity we get round this difficulty thanks to geometric arguments of some SPDEs under certain assumptions. Attraction of specific to Hamiltonian systems and by studying homo- the self-similar solution is shown by applying random in- clinic orbits with many loops. variant manifold theory (in almost sure sense) and a diffu- sion approximation (in distribution) in the case of additive Tiphaine J´ez´equel noise and stochastic advection respectively. LMPT, Universit´edeTours [email protected] Wei Wang Nanjing University [email protected] Patrick Bernard CEREMADE, Universit´e Paris - Dauphine [email protected] MS121 Exploring Experimental Paths for Reliable Mathe- ric Lombardi matical Models of Friction Institut de Math´ematiques de Toulouse Universit´e Paul Sabatier, Tolouse, France Structural vibration controlled by interfacial friction is [email protected] widespread, ranging from earthquakes and violin strings, to vehicle brake squeal and friction dampers in gas tur- bines. To predict, control or prevent these systems’ be- MS120 haviours, a constitutive description of frictional interac- Slow Manifolds for a Nonlocal Spde tions is inevitably required. We shall explore the validity of friction models from the nonlinear dynamics of a driven This work is concerned with invariant manifolds for a forced single degree of freedom oscillator in view of recent slow-fast nonlocal stochastic evolutionary system quanti- experimental data gathered from the Cambridge pin-on- fied with a scale paramenter. Under suitable conditions, it disc experiment. is proved that an invariant manifold exists. Furthermore, it is shown that if the scale paramenter tends to zero, the Thibaut Putelat invariant manifold tends to a slow manifold which captures University of Bristol long time dynamics. [email protected]

Lu Bai Huazhong University of Science and Technology MS121 [email protected] Testing of a Spacecraft Structure with Non-Smooth Nonlinearities

MS120 The dynamics of the SmallSat, a real-life spacecraft pos- Slow Manifolds and Interface Motion for Stochastic sessing a complex isolation device with multiple nonsmooth PDEs nonlinearities, is investigated. Experiments show that non- linearities induce modal interactions between modes with We consider examples of spatially one-dimensional stochas- non-commensurate linear frequencies. A model of the tic partial differential equations like the Cahn-Hilliard structure with a simplified description of the nonlinear con- equation perturbed by additive noise, and study the dy- nections is first built using techniques available in indus- namics of interfaces for the stochastic model. The dynamic try. Numerical continuation is then exploited to compute of the stochastic infinite dimensional system is given by nonlinear normal modes and uncover the interaction phe- the motion along a finite dimensional deterministic slow nomena which can jeopardize the structural integrity. manifold M parametrized by the interface positions. Main results include stochastic stability for M, and a derivation Ludovic Renson of an effective equation for the interface positions. Joint Universit´edeLi`ege work with Dimitra Antonopoulou and Georgia Karali. [email protected]

Dirk Bl¨omker J.P. Noel, G. Kerschen DS15 Abstracts 203

University of Liege [email protected] [email protected], [email protected]

MS122 MS121 Stability of Traveling Waves in a Model for a Thin Liquid Film Flow Painlev´e Paradox: Lessons That We Do Not Learn from Simple Examples We consider a model for the flow of a thin liquid film down an inclined plane in the presence of a surfactant, which is Painlev´e's paradox (non-uniqueness and non-existence in known to possess various families of traveling waves. We the dynamics of rigid multi-body system with friction) is use a combination of analytical and numerical means to usually studied via single-contact examples, which exhibit show that the spectra of these waves are within the closed a limited variety of interesting dynamics. In this talk, I left-half complex plane. show new phenomena based on the analysis of systems with two unilateral, sliding contacts. These include seemingly Vahagn Manukian regular systems, which fail to follow a unique and existing Miami University Hamilton solution; and systems, in which the lack of solutions is not [email protected] resolved by 'tangential impacts'.

Peter L. Varkonyi MS122 Budapest University of Technology and Economics Oscillons Near Hopf Bifurcations of Planar Reac- [email protected] tion Diffusion Equations

Oscillons are planar, spatially localized, temporally os- MS121 cillating, radially symmetric structures often arising near forced Hopf bifurcations.Using spatial dynamics, we show Nonlinear Dynamics and Bifurcations of Rotor- that the dynamics on the center manifold of a periodically Stator Contact in Rotating Machines forced reaction diffusion equation (fRD) near a Hopf bi- furcation can be captured by the forced complex Ginzbur- A modified Jeffcott rotor model is studied that includes the gLandau equation (fCGL). Thus, oscillon solutions to the effects of coupled lateral-torsional deformations and rotor- fRD can be thought of as a foliation over localized solutions stator contact with friction. Numerically, bifurcations are to the fCGL. found that cause instability or lift-off of either forward or backward whirl. The results are compared for three differ- Kelly Mcquighan ent nonsmooth friction laws and are favorably compared Boston University with analytical predictions. Implications of the results for [email protected] the dynamics of drill-strings and turbomachinery are dis- cussed. Bjorn Sandstede Division of Applied Mathematics Nicholas Vlajic Brown University Quantum Measurement Division: Force and Mass Group bjorn [email protected] National Institute of Standards and Technology [email protected] MS122 Alan R. Champneys The Entry-exit Function and Geometric Singular University of Bristol Perturbation Theory [email protected] For small >0, the systemx ˙ = ,˙z = h(x, z)z,with Michael Friswell, Kiran Vijayan h(x, 0) < 0forx<0andh(x, 0) > 0forx>0, ad- Swansea University mits solutions that approach the x-axis while x<0and [email protected], [email protected] are repelled from it when x>0. The limiting attraction and repulsion points are given by the well-known entry-exit function. For h(x, z)z replaced by h(x, z)z2, we explain this MS122 phenomenon using geometric singular perturbation theory. The linear case can be reduced to the quadratic case, which Nonlinear Waves in a Lugiato-Lefever Model is related to periodic traveling waves in a diffusive predator- prey model. The Lugiato-Lefever equation is a cubic nonlinear Schr¨odinger equation with damping, detuning and driv- Peter De Maesschalck ing force arising as a model in nonlinear optics. Steady Hasselt University waves of this equation are found as solutions of a four- [email protected] dimensional reversible dynamical system in which the evo- lutionary variable is the space variable. Relying upon tools Stephen Schecter from bifurcation theory and normal forms theory, we show North Carolina State University the existence of various types of steady solutions, includ- Department of Mathematics ing spatially localized and periodic solutions. Finally, we [email protected] discuss some stability properties of periodic solutions.

Mariana Haragus MS123 Universite de Franche-Comte Pattern-formation in Semiarid Vegetation: Using 204 DS15 Abstracts

Bifurcation Theory for Model Comparison Antonios Zagaris Universiteit Twente In semi-arid ecosystems, water is considered a limiting re- [email protected] source for vegetation growth. This principle gives rise to a variety of PDE models describing vegetation-water in- teractions that predict the formation of self-organized spa- MS123 tial patterns in vegetation communities as a response to Stripe Pattern Selection by Advective RD Systems: resource scarcity. We use bifurcation theory to identify ro- Resilience of Banded Vegetation on Slopes bust structures that persist across different models of this phenomenon. From this perspective, we find system behav- We study a Gray-Scott type system of PDEs that models iors that are robust to uncertainty in model choice, and we vegetation in (semi-)arid regions. Observations of stripe identify models that are not sensitive to small structural patterns along slope contours are widespread. We focus perturbations. on stripe break up into rectangles/hexagons. It is shown that an increase in slope/advection leads to an increase Sarah Iams of resilience/stability of vegetation stripes. The analytical Northwestern University results generalize to classes of systems. Evanston, IL [email protected] Eric Siero Leiden University, Mathematical Institute [email protected] MS123 Models of Patchy Invasion: A Mathematical Toy Arjen Doelman Or a New Paradigm? Mathematisch Instituut [email protected] A theory based on diffusion-reaction equations predicts the invasive species spread as a traveling population front sep- Jens Rademacher arating the invaded and non-invaded regions. However, it University of Bremen appears to be at odds with some recent observations. In [email protected] some cases, the spread takes place through formation of a distinct patchy spatial structure without any continuous boundary. I will revisit the traditional diffusion-reaction MS124 framework and show that the patchy spread is its inherent Input-Ouptut Analysis in Channel Flows and Im- property in case the invasive species is affected by predation plications for Flow Control or pathogens. The patchy spread described by a diffusion- reaction model appears to be a scenario of alien species The Navier-Stokes equations for channel flows are a pro- invasion ”at the edge of extinction”. I will also show that totype model for turbulent boundary layer flow control, patchy spread is not an exclusive property of the diffusion- specifically for the problem of skin-friction drag reduction. reaction systems but can be observed as well in different To carry out model-based control designs, control-oriented types of model. dynamical models of the processes to be controlled are needed. Such models need to contain the phenomena that Sergei Petrovskii are to be controlled and stabilized. We present an input- Department of Mathematics output analysis of channel flows, and control-oriented lin- University of Leicester earized models that contain much of the phenomenology of [email protected] bypass transition.

Bassam A. Bamieh MS123 UC Santa Barbara The Effect of Slow Spatial Processes in a [email protected] Phytoplankton-Nutrient Model

We consider a system of reaction-diffusion equations de- MS124 scribing the interaction of phytoplankton in the deep ocean Nematic Liquid Crystal Flow in a Microfluid: with its nutrient. Recently, we have studied bifurcations Topological Transitions and stability of two types of patterns exhibited by this PDE system. The result is two-fold. On the one hand, Motivated by recent experimental work by Sengupta and our analysis captures field observations, thereby validat- co-workers on flow of a nematic liquid crystal (NLC) within ing the model we used. On the other hand, our analysis a microfluidic, we consider flow of NLC within a channel, is of mathematical interest. In a formal derivation, using with homeotropic (perpendicular) anchoring on the direc- asymptotic methods, we extend a classic version of center tor field at the walls. We find that this setup admits two manifold reduction to a regime where the, usually neces- exact steady solutions, with distinct director topology; and sary, spectral gap condition is violated. With this tool, we that based on energetic arguments, as the flow rate is in- capture parameter regimes in which each of the patterns is creased, there is a transition from one solution to the other. stable and flourishes.

Lotte Sewalt Linda Cummings Leiden University Department of Mathematical Sciences [email protected] New Jersey Institute of Technology [email protected] Arjen Doelman Mathematisch Instituut Thomas Anderson [email protected] Caltech DS15 Abstracts 205

[email protected] [email protected]

Lou Kondic Department of Mathematical Sciences, NJIT MS126 University Heights, Newark, NJ 07102 Synchronization of Calcium Sparks and Waves [email protected] In this presentation, we show how membrane potential af- fects Ca sparks and waves, especially during delayed af- MS124 terdepolarizations (DADs). We use a physiologically de- Correlating Dynamical Structures with Forcing in tailed mathematical model to investigate individual factors 2D Flow which affect Ca spark generation and wave propagation. We found that depolarization promotes Ca wave propaga- Lagrangian Coherent Structures (LCSs) have been widely tion and hyperpolarization prevents it. We will discuss the studied in recent years, and have been shown to be a useful details of the underlying mechanisms in the talk. characterization of complex fluid flows. However, current methods to detect LCSs require knowledge of future in- Daisuke Sato formation, and it is not known how to generate LCSs on UC davis demand. As a step toward moving past simple observa- [email protected] tion, I will discuss the correlations between forcing in an experimental quasi-2D flow and the resulting LCSs. MS126 Nicholas T. Ouellette Yale University Nucleation and Dynamics of Spontaneous Ca Department of Mechanical Engineering and Materials Waves in Cardiac Cells Science [email protected] Spontaneous Calcium release (SCR) occurs when ion chan- nel fluctuations lead to the nucleation of calcium waves in cardiac cells. This phenomenon is important since it has MS124 been linked to various cardiac arrhythmias. However, to date it is not understood what determines the timing and Multi-Objective Optimal Control of Transport and location of the spontaneous events within cells. Here we Mixing in Fluids have developed a simplified model of SCR and analyzed a determinstic mean field limit sheds light on the essen- Aspects of controlling transport and mixing in fluid flows tial features of this phenomenon. We find that SCR is have received considerable scientific interest in the last few typically nucleated at preferred sites of the cell which can years. Here we describe a multi-objective optimal con- determined by studying the structure of eigenvectors of a trol framework for the optimization of advective processes class of Euclidean random matrices. Using this approach with respect to certain transport or mixing properties. We we estimate the timing of SCR in terms of physiological pa- demonstrate it with a number of example systems, which rameters such as the spatial arangement of calcium release may serve as simple models of microfluidic devices. units, and the local ion channel kinetics. Kathrin Padberg-Gehle Institute of Scientific Computing Yohannes Shiferaw TU Dresden California State University [email protected] Northridge [email protected] Sina Ober-Bl¨obaum University of Paderborn MS126 [email protected] Complex Dynamic Patterns of Voltage and Cal- cium in Mammalian Hearts MS126 Effects of Implementing Contraction to Calcium- Cardiac dynamics is govern with bidirectional coupling be- Voltage Models tween transmembrane-voltage (Vm) and free intracellular calcium (Cai). Altering this coupling it is known to be In this study we present a systematical methodology to the important precursor of different forms of cardiac ar- incorporate a contraction model (Negroni Lascano 1996) rhythmia and cardiac alternans as triggers for cardiac reen- into fourteen well known single cell electrophysiology (EP) try. We present our experimental method for simultaneous models. To evaluate how well these coupled electrome- measurements of Vm and Cai with a single sensor, and chanical (EM) models behave, we study them under pos- obtained experimental results of alternans and ventricu- textrasystolic pacing (PESP) protocol. We first compare lar fibrillation development in different mammalian hearts the dynamics between the new EM models and the original (pig, rabbit, cat). EP models then we compare the contractile strength of the new EM models with the experiment (Yue et al 1985). Ilija Uzelac,FlavioM.Fenton Georgia Institute of Technology Yanyan Ji,FlavioM.Fenton [email protected], Georgia Institute of Technology fl[email protected] [email protected], fl[email protected]

Richard Gray MS127 U.S. Food and Drug Administration Dynamic Information Routing in Complex Net- 206 DS15 Abstracts

works [email protected]

Abstract not available. Nicollette Ognjanovski Department of Molecular, Cellular and Developmental Christoph Kirst Biology Center for Studies in Physics and Biology University of Michigan Rockefeller University, US [email protected] [email protected] Sara Aton MS127 2Department of Molecular, Cellular and Developmental Unraveling Network Topology from Derivative- Biology Variable Correlations University of Michigan [email protected] A method of network reconstruction from the dynami- cal time series is introduced, relying on the concept of Michal Zochowski derivative-variable correlation. Using a tunable observable Department of Physics and Biophysics Program as a parameter, the reconstruction of any network with University of Michigan known interaction functions is formulated via simple ma- [email protected] trix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length compara- ble to the characteristic dynamical time scale. Our method MS128 also provides a reliable precision estimate. We illustrate the Rigorous Numerics for Symbolic Dynamics and method’s implementation via elementary dynamical mod- Topological Entropy Bounds els, and demonstrate its robustness to both model and ob- servation errors. Outer approximations of continuous, discrete-time sys- tems, or maps, incorporate bounded error and allow for Zoran Levnajic the rigorous extraction of dynamics via Conley Index the- Laboratory of Data Technologies ory and other tools. Recent advances, including joint work Faculty of Information Studies, Novo Mesto, Slovenia with W. Kalies, M. D. LaMar, R. Trevino and R. Frongillo, zoran.levnajic@fis.unm.si have extended the class of maps to which these methods may be applied and improved the types of results that one may obtain, specifically in terms of semi-conjugate sym- MS127 bolic dynamics and associated lower bounds on topological Reconstructing Network Connectivity by Triplet entropy. I will describe some of this recent work and show Analysis sample results.

We discuss recovery of the directional connectivity of a Sarah Day small oscillator network via the phase dynamics reconstruc- The College of William and Mary tion from multivariate data. Instead of the pairwise anal- [email protected] ysis, we analyse triplets of nodes and reveal an effective phase connectivity which is close but generally not equiva- Rafael Frongillo lent to a structural one. By comparing the coupling func- The University of California at Berkeley tions reconstructed from all possible triplets, we achieve a [email protected] good separation between existing and non-existing connec- tions, and thus reliably reproduce the network structure. MS128 Orbital Stability Investigations for Travelling Michael Rosenblum Waves in a Nonlinearly Supported Beam Potsdam University Department of Physics and Astronomy We consider the fourth-order problem [email protected] + ϕtt + ϕxxxx + f(ϕ)=0, (x, t) ∈ R × R ,

MS127 with a nonlinearity f vanishing at 0. Solitary waves ϕ = From Neural Dynamics to Network Properties and u(x + ct)satisfytheODE Cognitive Function  2  u + c u + f(u)=0 onR, It remains unclear to what extend structural and functional network measurements are complementary, or rather pro- and for the case f(u)=eu − 1, the existence of at least 36 vide orthogonal information about network state. We de- travelling waves was proved in [Breuer, Hor´ak, McKenna, veloped framework to capture neuronal correlations over Plum, Journal of Differential Equations 224 (2006)] by short timescales and use them to quantify large-scale func- computer assisted means. We investigate the orbital sta- tional connectivity shifts indicative of slower structural net- bility of these solutions via computation of their Morse work changes. We applied it to simulated as well as exper- indicies, which heavily relies on spectral bounds for the lin- imental data. We observed state dependent, network-wide earized operator, and using results from [Grillakis, Shatah, structural modifications and significant changes in network Strauss, Journal of Functional Analysis 74 (1987) and 94 stability, which is linked to behavior. (1990)]. We make use of both analytical and computer- assisted techniques. Daniel Maruyama Department of Physics Michael Plum University of Michigan Karlsruhe University (KIT) DS15 Abstracts 207

Germany on two recent findings: 1) The solution of the prototyp- [email protected] ical model proposed by Winfree in 1967. Using the Ott- Antonsen ansatz, the effect of pulse width on the onset of macroscopic synchronization is clarified. 2) For ensem- MS128 bles of quadratic integrate-and-fire neurons, a “Lorentzian The Parametrization Method in Infinite Dimen- ansatz” permits us to obtain exact low-dimensional firing- sions rate equations; in contrast to the current heuristic models used in neuroscience. Understanding the dynamics near the equilibrium solutions of a PDE is a first step towards a global dynamical scaf- Diego Paz´o fold. Their (un)stable manifolds are a powerful tool in this Instituto de Fisica de Cantabria (IFCA) analysis. We apply the Parameterization Method of Cabre, Santander, Spain Fontich and de la Llave in order to study finite dimensional [email protected] unstable manifolds in infinite dimensional phase space. We present both numerical implementations for some dissipa- Ernest Montbrio tive PDEs and a-posteriori theorems which provide rigor- Universitat Pompeu Fabra ous error bounds for the numerical approximations. Barcelona, Spain [email protected] Christian P. Reinhardt Department of Mathematics, VU University Amsterdam [email protected] Alex Roxin Centre de Recerca Matematica Bellaterra (Barcelona), Spain Jason Mireles-James [email protected] Departement of Mathematics Florida Atlantic University [email protected] MS129 Suppressing Complex Collective Behavior in a Net- MS128 work of Theta Neurons by Synaptic Diversity Rigorous Numerics for Some Pattern Formation A large heterogeneous network of globally coupled theta Problems neurons can demonstrate a range of collective behavior from simple equilibrium states to a collective rhythmic This talk is about applications of recently developed tech- state. Other complexity such as multistability, quasi- niques from rigorous computational dynamics to pattern periodicity, and macroscopic chaos can also occur. In the formation phenomena. We discuss the differences and sim- current work, we introduce heterogeneity in the neurons ilarities in the analytic setup of three examples, namely coupling strength and we find that synaptic diversity in- radially symmetric spots in the Swift-Hohenberg model, creases the robustness of equilibrium states and suppresses transitions between hexagonal spots and stripe patterns, the emergence of the collective rhythmic state and other and phase separation in diblock copolymers. These exam- complex network behavior. ples, which entail both ODEs and PDEs, also showcase the interplay between rigorous numerical methods and asymp- Lucas Lin totic techniques. Thomas Jefferson High School for Science and Technology [email protected] Jan Bouwe Van Den Berg VU University Amsterdam Department of Mathematics Ernest Barreto [email protected] George Mason University Krasnow Institute [email protected] MS129 Neural Field Models Which Include Gap Junctions Paul So George Mason University Neural field models are normally derived under the assump- The Krasnow Institute tion that connections between neurons are synaptic rather [email protected] than via gap junctions. I will show how to derive a neural field model from a network of “theta neurons” with both synaptic and gap junction connectivity. The derivation is MS130 exact in the limit of an infinite number of neurons. Mixed-Mode Bursting Oscillations (MMBOs): Slow Passage Through a Spike-adding Canard Ex- Carlo R. Laing plosion Massey University Auckland Mixed-Mode Bursting Oscillations (MMBOs) are solutions [email protected] of slow-fast dynamical systems that exhibit both small am- plitude oscillations (SAOs) and bursts consisting of one or multiple large-amplitude oscillations (LAOs). The name MS129 MMBO is given in analogy to Mixed-Mode Oscillations From Ensembles of Pulse-Coupled Oscillators to (MMOs), which consist of alternating SAOs and LAOs, Firing-Rate Models without the LAOs being organized into burst events. I will show how MMBOs are created naturally in systems that Ensembles of pulse-coupled oscillators are often encoun- have a spike-adding bifurcation, or spike-adding mecha- tered in biological and technological systems. We report nism, and in which the dynamics of one (or more) of the 208 DS15 Abstracts

slow variables causes the system to pass slowly through Yangyang Wang that bifurcation due to the presence of a folded node. University of Pittsburgh The analysis is carried out for a prototypical fourth-order [email protected] system of this type, which consists of the third-order Hindmarsh-Rose burster, known to have the spike-adding Vivien Kirk mechanism, and in which one of the key bifurcation pa- University of Auckland rameters also varies slowly. [email protected] Mathieu Desroches INRIA Paris-Rocquencourt Jonathan E. Rubin [email protected] University of Pittsburgh Department of Mathematics [email protected] Tasso J. Kaper Boston University Department of Mathematics MS130 [email protected] Averaging, Folded Singularities and Torus Canards in a Coupled Neuron Model Martin Krupa INRIA Paris-Rocquencourt We consider transitions between various bursting and tonic [email protected] spiking regimes in a coupled neuron model. Analysis of an averaged reduced system reveals the critical roles of folded singularities and the associated bifurcation scenarios, in- MS130 cluding a novel FSN III bifurcation; some of these bifur- An Organizing Center for Spatiotemporal Bursting cations correspond to torus bifurcations, yielding torus ca- nards, in the full system. We also show that the complete As the fundamental model of two timescales spatiotempo- set of bifurcations is captured in a canonical system that ral excitability, FitzHugh-Nagumo model has the interpre- can be treated analytically. tation of a normal form reduction organized by the hystere- sis singularity. We mimick the analog geometric construc- Kerry-Lyn Roberts tion in the universal unfolding of the winged cusp and ob- University of Sydney tain a three timescales model for spatiotemporal excitabil- [email protected] ity. Bursts and traveling bursts are shown to be the pro- totypical behaviors of the proposed model, in full analogy Jonathan E. Rubin with the spikes and traveling pulses of FitzHugh-Nagumo University of Pittsburgh model. Department of Mathematics Alessio Franci [email protected] Cambridge University England Martin Wechselberger [email protected] University of Sydney [email protected] Guillaume Drion Brandeis University Brandeis, MA MS131 [email protected] Unitary Representations of Diffeomorphisms: Halfway Between Koopmanism and Transfer Rodolphe Sepulchre Operator Theory University of Cambridge Cambridge, UK Koopmanism is derived from a representation of diffeo- [email protected] morphisms on the space of real valued functions. Dual to this pictures is the Frobenius-Perron operator where a diffeomorphism is represented as a linear operator on den- MS130 sities. In this talk we will present a unitary representa- Three Timescale Phenomena in Coupled Morris- tion of the diffeomorphism group on the Hilbert space of Lecar Equations half-densities. The resulting representation induces numer- ical advection schemes which will be useful in a variety of Theory for the analysis of systems with two timescales is scenarios. In particular, we may create spectral methods well established, but some dynamical phenomena are not which preserve the ring structure of functions, conserve captured by two timescale models and less is understood total mass, deform vector fields, and more. Such struc- about how to efficiently study systems with three or more ture preservation is important as one considers problems timescales. Motivated by applications in neural dynamics, in higher dimensions and requests qualitative accuracy in we study a pair of Morris-Lecar systems coupled so that exchange for numerical precision. there are three timescales in the full system. We identify complex oscillations that appear to be intrinsically three Henry O. Jacobs timescale phenomena, and use geometric singular pertur- Imperial College London bation theory to explain the mechanisms underlying these Mathematics solutions. [email protected] Pingyu Nan University of Auckland MS131 [email protected] Optimal Control Design and Value Function Esti- DS15 Abstracts 209

mation for Nonlinear Dynamical Systems Massachusetts Institute of Technology [email protected] This presentation considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state MS132 and box input constraints. We propose a sequence of sum- Stochastic Center Manifolds Without Gap Condi- of-squares (SOS) approximations of this problem obtained tions by first lifting the original problem into the space of mea- sures with continuous densities and then restricting these The existence of invariant manifolds requires that the spec- densities to polynomials. These approximations are tight- trum of linear part of a deterministic system or stochastic enings, rather than relaxations, of the original problem system contains large gaps. However, for some dynamical and provide a sequence of rational controllers with value systems, the condition of spectral gap condition is not sat- functions associated to these controllers converging (under isfied. In this case, it is still unknown whether there exists some technical assumptions) to the value function of the invariant manifolds. This paper concerns the center man- original problem. ifolds of the stochastic systems without the spectral gap Milan Korda condition. Ecole Polytechnique Federale de Lausanne milan.korda@epfl.ch Xiaopeng Chen Peking University [email protected] MS131 Transfer Operator Methods for Stability Analysis and Control MS132 How to Quantify Non-Gaussian Stochastic Dynam- Linear transfer Perron-Frobenius operator-based methods ics? are developed for global stability analysis and control de- sign of deterministic and stochastic nonlinear systems. The Dynamical systems arising in engineering and science are transfer operator-based Lyapunov measure is introduced often subject to random fluctuations, which may be Gaus- as a new tool to verify weaker set-theoretic notion of al- sian or non-Gaussian described by Brownian motion or most everywhere stability. Just as an invariant measure a-stable Levy motion, respectively. Non-Gaussianity of is a counterpart of the attractor (recurrence), this mea- the noise manifests as nonlocality at a macroscopic level. sure is demonstrated as a stochastic counterpart of stabil- Stochastic dynamical systems with a-stable Levy motions ity (transience). The Lyapunov measure is shown to be have attracted a lot of attention recently. The non- dual to the Lyapunov function. In addition to the theo- Gaussianity index a is a significant indicator for various retical results, we also present a computational method for dynamical behaviors. The speaker will present a few as- the approximation of the Lyapunov measure and almost pects of non-Gaussian stochastic dynamical systems, high- everywhere stabilizing feedback controller. These compu- lighting some delicate and profound impact of noise on dy- tational methods are based on set-oriented numerical ap- namics. Then, he will focus on understanding stochastic proaches. The linear nature of the framework provides lin- dynamics by examining certain deterministic quantities. ear programming-based computational methods for finite dimensional approximation of the Lyapunov measure and Jinqiao Duan stabilizing controller. Institute for Pure and Applied Mathematics UCLA Umesh Vaidya [email protected] Iowa State University [email protected] MS132 MS131 Random Dynamical Systems for Non-Densely De- Numerical Advection of Probability Densities for fined Evolution Equations High Dimensional Systems We consider abstract random evolution equations given by Understanding the effect of propagating uncertainty in ini- tial condition through dynamical systems is critical while  x (t)=Ax(t)+F (θtω,x(t)),x(0) = x0 ∈ D(A). (1) engineering verifiably safe systems. Given its importance, many numerical methods have been proposed to advect probability densities over an initial condition set by care- Here, we suppose that A is a non-densely defined linear fully manipulating nonnegative valued functions and densi- operator. Therefore, the C0-semigroup approach no longer ties. This management of nonegative objects unfortunately applies. Such situations can occur for instance due to non- restricts the applicability of these numerical methods to linear boundary conditions. By using integrated semigroup low dimensional dynamical systems. In this talk, I de- theory, we can show under suitable assumptions, the exis- scribe a method to address this shortcoming by developing tence of a random dynamical system for the above equation a linear advection equation over half densities, which can and discuss its asymptotic behavior. Finally, we analyze be thought of as the square root of classical nonnegative a class of non-densely defined stochastic differential equa- densities. This construction allows us to prove a rate of tions driven by a Banach-space valued Brownian motion. convergence for various numerical methods and allows us Our aim is to construct an Ornstein-Uhlenbeck process, to successfully advect smooth probability densities through which allows us to reduce the stochastic problem into a high dimensional systems. pathwise one. Ram Vasudevan Alexandra Neamtu University of California Berkeley Friedrich-Schiller-University Jena 210 DS15 Abstracts

[email protected] can be treated as constant if the time step is sufficient small.

MS133 Xiaosun Wang Lessons Learnt from the Two-Ball Bounce Problem Wuhan University China I revisit a popular classroom demonstration where a light [email protected] rigid body and a larger heavier ball are vertically aligned and dropped together. Experimental results obtained us- Jim Barber ing a high-speed camera are compared to a discrete model University of Michigan using Newtonian restitution, showing poor agreement as [email protected] the separation distance becomes small. An alternative model based on membrane theory is developed and com- pared favourably to experimental data in the limits of very MS134 small separation distance and mass ratio. Stability of Combustion Fronts in Hydraulically Yani Berdeni Resistant Porous Media University of Bristol We study front solutions of a system that models combus- [email protected] tion in porous media. The spectral stability of the fronts is studied on the linear and nonlinear level. For the spectral MS133 stability analysis we use a combination of energy estimates and numerical Evans function computations. Predicting Conditions for Self-sustained Vibration in Drillstrings Anna Ghazaryan Miami University High amplitude vibration in drillstrings is often the result [email protected] of a self-sustained regime of vibration such as torsional stick-slip oscillation; forward whirl; or backward whirl. The nonlinear interactions underlying these regimes come MS134 from bit-rock interaction and side-wall contact. We present a novel approach for modelling these regimes: assuming lo- Invasion Fronts in Systems of Reaction Diffusion cal nonlinearity, we derive conditions necessary to sustain a Equations given regime once it has already initiated. Results are nu- We study invasion speeds in a system of coupled Fisher- merically validated and give insight into each phenomenon. KPP equations. For certain parameter regimes we prove Tore Butlin that the speed selected by compactly supported initial data University of Cambridge is faster for the coupled system than for the uncoupled [email protected] one. The proof relies on the construction of sub and super solutions.

MS133 Matt Holzer Department of Mathematics Contact and Friction Within Geometrically Exact George Mason University Shell Theory - Modeling Microslip and Dissipation [email protected] in Structural Systems

We consider the representation of the dissipation due to frictional interfaces within large-scale structural systems. MS134 In this work contact and friction are incorporated within An Overview of Evans Function Computation geometrically exact shell theory, providing insight into the relationship between the observed dissipation and the load- We give an overview of Evans function and the numerical ing characteristics on the shell. Finally, the use of such techniques used to compute it. We provide a mini-tutorial formulations as a basis for reduced-order modeling and ex- on STABLAB, a MATLAB-based toolbox for Evans func- tensions to the larger problem of structural damping are tion computation, and show how to avoid some of the highlighted. common pitfalls that arise in Evans function computation. There are also a number of best practices that we high- D Dane Quinn light, noting that there are many variations on methods University of Akron and formulations. Different situations call for different ap- Dept of Mechanical Engineering proaches. [email protected] Jeffrey Humpherys Brigham Young University MS133 jeff[email protected] A New Semi-Analytical Algorithm for Two- Dimensional Coulomb Frictional System MS134 A closed form solution for the trajectory of a planer par- Orbital Stability of Waves Traveling Along Vortex ticle loaded by constant external force with Coulomb fric- Filaments tion has been proposed. Together with analytical patches close to slip/stick transitions, this solution has been em- By the term vortex filament, we mean a mass of whirling ployed to build a new semi-analytical algorithm for two- fluid or air (e.g. a whirlpool or whirlwind) concentrated dimensional frictional system subjected to time-varying ex- along a slender tube. The most spectacular and well-known ternal loads under the assumption that the external loads example of a vortex filament is a tornado. A waterspout DS15 Abstracts 211

and dust devil are other examples. In more technical ap- University of Pittsburgh plications, vortex filaments are seen and used in contexts Department of Mathematics such as superfluids and superconductivity. One system of [email protected] equations used to describe the dynamics of vortex filaments is the Vortex Filament Equation (VFE). The VFE is a sys- Yasuhiko Jimbo tem giving the time evolution of the curve around which Graduate School of Engineering the vorticity is concentrated. In this talk, we develop a The University of Tokyo framework for studying the stability solutions of the VFE, [email protected] based on the correspondence between the VFE and the NLS provided by the Hasimoto map. We use this frame- Kiyoshi Kotani work to establish the orbital stability of certain classes of Research Center for Advanced Science and Technology solutions including solitons and closed solutions taking the The University of Tokyo form of torus knots. [email protected] St´ephane Lafortune College of Charleston PP1 [email protected] A Solution of Linear Programming Problems with Interval Coefficients PP1 In this talk, we consider a linear programming problem The Breakup of Invariant Tori in 4-D Maps Using where the coefficients are interval. For these problems, we the Slater’s Criterion cannot apply the technique of the classical linear program- ming directly. We focus on a satisfactory solution approach In the late of 40s, N. B. Slater proved that an irrational based on the inequality relations that was introduced by translation over an unity circle can take at most three dif- Alolyan and to solve the interval linear programming prob- ferent return counts to a connected interval (δ<1). In ad- lem. In order to solve such a problem, we present an al- dition, these three recurrence times are expressible by the gorithm that find the solution of such a problem and show continued fraction expansion of the irrational number used the efficiency of the algorithm and present a numerical ex- to the translation. This remarkable result has an immedi- ample. ate connection with invariant tori, whose rotation number in the bi-dimensional phase space is also irrational and can Ibraheem Alolyan be related to a motion over the circle. Thus, the eval- King Saud University uation of three recurrence times has been used to predict [email protected] breakup of such invariant tori in several 2-D dynamical sys- tems. Here we introduce the Slater’s theorem in the con- text of higher dimension Hamiltonian systems to estimate PP1 the breakup of invariant tori in a 4-Dimensional symplectic Developing a Model Approximation Method and map. Parameter Estimates for a Solar Thermochemistry Application Celso Abud University of Sao Paulo We will show the model and software development process [email protected] used in creating a robust parameter optimizer for a solar reactor. The basic reaction model is numerically difficult Ibere L. Caldas to solve, so several proprietary elements of code were de- Institute of Physics veloped to interface with standard optimization routines. University of Sao Paulo Integrating complex toolboxes and non-standard code led [email protected] to several insights into good development practices which will be highlighted.

PP1 William D. Arloff Theta Model for Quartic Integrate-and-Fire Neu- Valparaiso University ron Model william.arloff@valpo.edu

The theta model is convenient to investigate the popula- Karl Schmitt tion dynamics of coupled noisy neurons due to the periodic Valparaiso University boundary conditions of the corresponding Fokker-Planck Department of Mathematics equation. However, quantitative relationships between the [email protected] theta model and conductance-based neuron models has not been thoroughly explored. We propose a version of Luke Venstrom, Leandro Jaime the theta model derived from a quartic integrate-and-fire Valparaiso University model, which has quantitatively equivalent dynamics to Dept. of Mechanical Engineering biophysically realistic Wang-Buzsaki model. We also ana- [email protected], [email protected] lyze the population dynamics of this new model.

Akihiko Akao, Yutaro Ogawa PP1 Graduate School of Frontier Sciences Hamiltonian Hopf Bifurcations in Schrdinger The University of Tokyo Trimers [email protected], [email protected] The cubic nonlinear Schrdinger equation is fundamentally important in the physics of waves, arising in optical fibers, Bard Ermentrout waveguides, Bose-Einstein condensates, and water waves. 212 DS15 Abstracts

We investigate the phase space of the three-mode discrete [email protected] NLS in the weakly nonlinear regime. We enumerate the families of standing waves and use normal forms to describe several families of relative periodic orbits whose topologies PP1 change due to Hamiltonian Hopf bifurcations and others. Analyzing Cycling Dynamics in Stochastic Systems

Casayndra H. Basarab We consider a Langevin model where external noise causes New Jersey Institute of Technology random switching between metastable states. A chain of [email protected] these states, such as those found in a multi-well potential, enables cycling dynamics. Switching times are found us- ing a variational approach. Additionally, a probabilistic Roy Goodman argument is used to understand the cycling dynamics. An- NJIT alytical results agree well with numerical simulations for a NJIT range of well depths and noise intensities. [email protected] Pralhad Burli Montclair State University PP1 [email protected] Computing the Optimal Path in Stochastic Dynam- Lora Billings ical Systems Montclair State University Dept. of Mathematical Sciences In stochastic systems, we are often interested in quanti- [email protected] fying the optimal path that maximizes the probability of switching between metastable states. However, in high- Eric Forgoston dimensional systems, the optimal path is often extremely Montclair State University difficult to approximate. We consider a variety of problems Department of Mathematical Sciences from population biology and demonstrate a constructive [email protected] methodology to quantify the optimal path using a com- bination of finite-time Lyaponuv exponents, statistical se- lection criteria, and a Newton-based iterative minimizing PP1 scheme. Limit Cycles in a Simplified Basal Ganglia Model

Martha Bauver Muscle rigidity associated with Parkinson’s disease is Montclair State University thought to be correlated with the loss of dopamine and [email protected] the emergence of beta oscillations in the basal ganglia. As dopamine-producing neurons die off, synaptic connection Lora Billings strengths change leading to a favoring of the Indirect Path- Montclair State University way. Though a model of the entire basal ganglia process is Dept. of Mathematical Sciences quite complicated, we show that a simplified version can ex- [email protected] hibit both steady-state and limit cycle behavior by changes in connection strength alone. Eric Forgoston Michael Caiola Montclair State University Rensselear Polytechnic Institute Department of Mathematical Sciences [email protected] [email protected] Mark Holmes Rensselaer Polytechnic Institute PP1 [email protected] Effects of Quasi-Steady-State Reduction on Bio- physical Models with Oscillations PP1 Many mathematical models of biological systems possess Mathematical Modelling of Spatial Sorting and multiple time scales. A common first step in the analysis Evolution in a Host-Parasite System of such models is the elimination of one or more of the We examine the spatial self-structuring of traits in both a fastest variables via quasi-steady-state reduction (QSSR). cane toad population and lungworm parasite population, However, this process sometimes leads to changes in the which evolves with the cane toad population. In particular, dynamics by introducing or removing bifurcations. We dis- the traits we focus on are dispersal ability for the cane toad cuss the persistence of Hopf bifurcations under QSSR and population and both prepatent period and larval size for show examples of qualitative changes to oscillatory dynam- the lungworm parasite population. Along with the spatial ics that can be induced by QSSR. self-structuring of these traits, our results confirm observa- tions made in empirical studies; particularly, that there is Sebastian D. Boie, Vivien Kirk a noticeable lag between the host and parasite population, University of Auckland that older populations regress to lower dispersal speeds and [email protected], [email protected] that “spatial sorting” of dispersal ability can still occur with a disadvantage in reproductivity and/or survival in James Sneyd more motile individuals. Moreover, we find that such a University of Auckland disadvantage in reproductivity and/or survival is unlikely Department of Mathematics to be large if spatial sorting is to have a noticeable effect DS15 Abstracts 213

on the rate of range expansion, as it has been observed to Engineering, have over the last 60 years in northern Australia. University of Aberdeen, AB24 3UE, Aberdeen, Scotland, UK. Matthew H. Chan [email protected] University of Sydney [email protected] PP1 Gregory Brown, Richard Shine Modeling the Lymphocytic Choriomeningitis School of Biological Sciences, University of Sydney Virus: Insights into Understanding Its Epidemiol- [email protected], [email protected] ogy in the Wild

Peter S. Kim The lymphocytic choriomenigitis virus (LCMV) is a University of Sydney rodent-spread virus commonly recognized as causing neu- School of Mathematics and Statistics rological disease that exhibits asymptomatic pathology. [email protected] We looked to construct an epidemiological model of a mouse population to better understand how this virus can remain endemic. We used an SIRC model that incorpo- PP1 rated gender dynamics as to capture the primary aspects of the disease, and establish some initial findings under Using Tangles to Quantify Topological Mixing of which the carriers remained stable. Fluids Christy Contreras Topological entropy (TE), a measure of topological mixing, Arizona State University can be studied by the braiding of ghost rods. We study the [email protected] system of Grover et al. [Chaos 22,043135 (2012)] using a heteroclinic tangle. In this approach, we explain TE through intersecting stable and unstable manifolds using PP1 homotopic lobe dynamics (HLD). The HLD method uses Causal Relationships Between Time Series: Gener- ghost rods placed on heteroclinic orbits, which allows us alizing Takens’ Theorem to a Dynamical Network to compute TE in excess of that given by simple periodic braiding. We consider a set of scalar time series measured from a dynamical system evolving on an invariant manifold M. Qianting Chen Takens’ Theorem says that the state space reconstruction University of California, Merced (SSR) for a time series is generically diffeomorphic to M. [email protected] A non-generic SSR does not faithfully represent M.We prove that it generically represents the dynamics of a feed- Sulimon Sattari back system within the larger dynamical system. Time University of California, Merced series SSRs are compared to recover potential causal rela- School of Natural Sciences tionships between feedback systems. [email protected] Bree Cummins Kevin A. Mitchell Department of Mathematics University of California, Merced Tulane University Physics [email protected] [email protected] Tomas Gedeon Montana State University PP1 Dept of Mathematical Sciences New Computational Tools for Non-Smooth Dy- [email protected] namical Systems Kelly Spendlove We will present development of new computational tools Rutgers University capable to comprehensively analyse the non-smooth dy- [email protected] namical systems. They will allow for high accuracy and speed brute force numerical simulation of dynamical sys- tems having various types of discontinuities. On the same PP1 platform a powerful and convenient path-following mod- Regular Acceleration from Low Initial Energies in ule is being developed allowing for modelling and analysis a Magnetized Relativistic System of non-smooth systems efficiently. As an example, we will present the modelling and analysis of soft impact oscilla- We consider a relativistic particle interacting with a uni- tors. The ultimate aim of the project is to take the state- form magnetic field and a stationary electrostatic wave. of-art of computational tools available for non-smooth sys- According to the parameters of the wave, triangular islands tems a step further. appear in the low energy region of phase space. In this scenario, a particle with initial energy close to its rest en- Antonio S. Chong ergy is accelerated and achieves a considerable final energy. Centre of Applied Dynamic Research, CADR We obtain analytically the parameter region for which the University of Aberdeen, Scotland, United Kingdom particle can be regularly accelerated from very low initial [email protected] energies.

Marian Wiercigroch Meirielen C. De Sousa Centre for Applied Dynamics Research, School of Instituto de Fsica, Universidade de So Paulo, Brazil 214 DS15 Abstracts

[email protected] complex Ginzburg Landau and Cahn-Hilliard equations.

Iber L. Caldas Ryan Goh,ArndScheel Instituto de Fsica, Universidade de So Paulo University of Minnesota [email protected] [email protected], [email protected]

Fernanda Steffens Deutsches Elektronen-Synchrotron, Germany PP1 fsteff[email protected] Pattern Sequences as Early-warning Signs of Crit- ical Transition in Models of Dryland Vegetation Renato Pakter, Felipe Rizzato Instituto de Fsica, Universidade Federal Rio Grande do Regular spatial patterns (resembling tiger stripes and leop- Sul ard spots) occur in the vegetation of many dryland ecosys- [email protected], [email protected] tems, and are hypothesized to be a self-organized response to water scarcity. Numerous partial differential equation PP1 models of vegetation-water interactions based on this hy- ∞ pothesis have been proposed to investigate how patterned Estimating the L -Norm of Linear Solutions of ecosystems may respond to increased water scarcity. As Cahn-Hilliard a precipitation parameter decreases in value, a sequence ∞ of patterns, gaps → labyrinths → spots, is observed in Using a simple toy model we approach the problem of L - simulations of many of these models. Observations of this bounds on linear solutions of the strong subspace of Cahn- kind have led this sequence to be suggested as an early- Hilliard solutions and relate it to its pattern development. warning sign of dryland vegetation collapse. In a previous bifurcation theoretic analysis, we analytically studied tran- sitions between two pattern-forming instabilities to assess Philipp D¨uren → → Universit¨at Augsburg the generic robustness of the “gaps labyrinths spots’ [email protected] sequence. We found that alternative sequences of patterns are possible in this generic setting, and we conjectured that a calculable quantity signals the appearance of the stan- PP1 dard pattern transition sequence in the models. Here, we test this conjecture in two widely studied vegetation models Spike Adding in Transient Dynamics through weakly nonlinear analyses and numerical simula- Many mathematical models of neuron activity exhibit com- tions. We find that our conjecture holds in these models plex oscillations in response to stimulus from an applied for the space of parameter values considered. In addition, current or from other neurons. We consider the effect of we find that a sequence involving only spot patterns occurs a single short stimulus on a neuron that is otherwise qui- as a common alternative to the standard sequence. escent, focussing on the transient response induced by the stimulus. We use numerical continuation methods and ex- Karna V. Gowda,YuxinChen ploit the presence of different time scales in the model to ex- Northwestern University plain how the oscillatory pattern in the transient response [email protected], depends on parameters. [email protected]

Saeed Farjami Sarah Iams The University of Auckland Northwestern University [email protected] Evanston, IL [email protected] Hinke M. Osinga University of Auckland Mary Silber Department of Mathematics Northwestern University [email protected] Dept. of Engineering Sciences and Applied Mathematics [email protected] Vivien Kirk University of Auckland [email protected] PP1 Rigorous Computation of Radially Symmetric Sta- PP1 tionary Solutions of Pdes Front-Dynamics and Pattern Selection in the Wake of Triggered Instabilities We present a rigorous numerical method for proving the ex- istence of radially symmetric solutions of stationary PDEs Pattern-forming fronts are often controlled by some ex- on the entire space. By combining numerical methods with ternal stimulus which progresses at fixed speed, rendering functional analytic estimates, we show the existence of a the medium unstable. Such ”triggers” control dynamics solution by showing the existence of a fixed point of an in two generic ways corresponding to pushed and pulled equivalent fixed-point problem T (x)=x.Weshallap- fronts. The former is governed by oscillatory nonlinear in- ply this method to a previously unsolved Ginzburg-Landau teractions, leading to hysteresis and multi-stability. The type equation. latter is governed by absolute spectra and interacts mono- tonically. We use heteroclinic bifurcation and functional Chris M. Groothedde analytic techniques to study prototypical examples in the VU University Amsterdam DS15 Abstracts 215

[email protected] between the two boilers. An invariant manifold represent- ing steady operating condition of the system is located, and its existence and persistence are investigated. This clarifies PP1 the stability aspect of the steam supply system. Dynamics of Register Transitions in Human Vocal Fold Modeling Hikaru Hoshino Department of Electrical Engineering, Kyoto University There are several theories as to the mechanism of regis- [email protected] ter transitions in the human voice. The suddenness of the change under smooth variations of aerodynamic and Yoshihiko Susuki biomechanical parameters suggests a bifurcation-like phe- Kyoto University / JST-CREST nomenon with hysteresis. Often, the mechanics of the hu- [email protected] man vocal folds are modeled by a simple system of coupled oscillators. We show in theory and simulations what dy- namical phenomena in these systems could generate such PP1 transitions. Defects in Spatially Extended Systems

Jesse Haas We look at the effects of defects on pattern formation as GIPSA-Lab, Institut Polytechnique de Grenoble a perturbation problem. We present a few examples of [email protected] spatially extended pattern forming systems, and explain why regular perturbation theory fails due to critical con- tinuous spectrum. We show how Kondratiev spaces can PP1 help alleviate this difficulty: the linearization at periodic A Mathematical Model of Saliva Secretion and Cal- patterns becomes a Fredholm operator, albeit with nega- cium Dynamics tive index. Together with far-field matching procedures, 2+ we obtain deformed stripe patterns or pacemakers using Oscillations in free intracellular calcium (Ca )concen- implicit function type continuation. tration carry signals that control cellular processes such as neuronal firing and secretion. Experimental data show that 2+ Gabriela Jaramillo oscillations of Ca in certain salivary duct cells are cou- University of Minnesota pled to oscillations in inositol trisphosphate (IP3). I will [email protected] describe a recently constructed model of Ca2+ dynamics in salivary duct cells that captures important dynamical Arnd Scheel features of the data and shows how the dynamics of IP3 affects certain features of the calcium oscillations. University of Minnesota School of Mathematics Jung Min Han, James Sneyd, Vivien Kirk [email protected] University of Auckland [email protected], [email protected], [email protected] PP1 Delayed Feedback Model of Axonal Length Sensing

PP1 It has been proposed that an axon is able to gauge its Mixed-Mode Oscillations and Twin Canards own length based on the frequency of the oscillations of a molecular motor-based retrograde chemical signal. The We consider mixed-mode oscillations (MMOs), featuring frequency is inversely related to the length of the axon. a mix of small and large amplitudes, in dynamical sys- We model the chemical oscillations using a system of delay tems with one fast and two slow variables. These oscilla- differential equations and reproduce this relationship. We tions are organised by canard orbits, which are intersection then investigate the behavior of these chemical signals as curves between attracting and repelling two-dimensional we model motor dynamics using stochastic partial differ- slow manifolds. We show how paired or twin canards with ential equations. the same number of small oscillations arise in fold bifur- cations of slow manifolds, and what this implies for the Bhargav R. Karamched observed MMOs. University of Utah Salt Lake City, UT Ragheb Hasan [email protected] University of Auckland [email protected] Paul C. Bressloff University of Utah Hinke M. Osinga, Bernd Krauskopf Department of Mathematics University of Auckland bressloff@math.utah.edu Department of Mathematics [email protected], [email protected] PP1 Nonlinear Dynamical Systems in Finance PP1 A Dynamical Analysis of Steam Supply Network Dynamical system is very popular and important issue in Based on Invariant Manifold todays World. It is important to understand systems in geology, mathematics, microbiology, biology, computer sci- In this presentation, we analyze dynamics of heat supply in ence, economics, engineering, finance, algorithmic trading, a simple steam supply system. The system consists of two meteorology, philosophy, physics, politics, population dy- steam boilers and a steam pipe which enables heat transfer namics, psychology, meteorology, robotics etc. Then with 216 DS15 Abstracts

having clear understanding about system we can make bet- [email protected] ¡[email protected]. ter predictions. In poster, definition and usage areas of nonlinear dynamical system and chaos will be covered. Main aim is understanding the dynamical system in fi- PP1 nance. Coupling Methods As a Tool for Sensitivity Anal- ysis of Stochastic Differential Equations Deniz K. Kili¸c SIAM student membership,student at Middle East Under appropriate assumptions of Ergodicity, the expected Technical Uni value of observables for dynamical systems can be approx- versity,Institute of Applied Mathematics(member of imated by time averages. The introduction of stochas- SIAM) tic forcing in the form of additive white noise can result [email protected] in greatly increased varience of the observable estimates, making sensitivity analysis a delicate task. In this setting, coupling methods can be employed as a tool for varience re- PP1 duction. The methods and their applications to Stochastic Polyrhythmic Synchronization in Modular Net- Differential Equations will be discussed. works Andrew Leach CPGs comprised of coupled interneuron circuits underlie University of Arizona wide ranges of natural rhythmic behaviors. Phase lag [email protected] return maps describing polyrhythmic behavior in three- node reciprocally-inhibitory Fitzhugh-Nagumo type net- works characterize regimes of robustness and stability sim- PP1 ilar to natural patterns. Further, we examine complex Transient Dynamics in Ensemble of Inhibitory rhythm generation in modular network settings coupling Coupled Rulkov Maps two such networks. Transition from small local-networks to so-called network-of-networks permits within-circuit multi- We study numerically three Rulkov maps with mutual in- phase coordinated pattern storage that may underlie learn- ertia inhibitory couplings. We study numerically different ing and memory of more complex motor rhythm patterns. dynamical regimes that can be obtained in this ensemble by governing coupling parameters, in particular, sequen- tial activity regime and multistable regime, and bifurcation Jarod Collens transition from one regime to another. Georgia State University Neuroscience Institute and Mathematics Department Tatiana A. Levanova, Grigory Osipov [email protected] Lobachevsky State University of Nizhny Novgorod [email protected], [email protected] Justus T. Schwabedal Neuroscience Institute PP1 Georgia State University Complex Collective Behavior in a Network of [email protected] Theta Neurons is Suppressed by Synaptic Diver- sity Andrey Shilnikov Neuroscience Institute and Department of Mathematics In the wake of a study that examined the collective dy- Georgia State University namics of a large network of uniformly coupled Type 1 [email protected] neurons, we explored how the patterns of macroscopic be- havior change with respect to alterations in different neu- Drake Knapper ron parameters of a model that includes realistic biologi- Georgia State University cal diversity through connection variability. Our analysis [email protected] demonstrated that heterogeneity in coupling strength in- creases the robustness of equilibrium states and increasing synaptic diversity suppresses the emergence of the collec- PP1 tive rhythmic state. Discriminating Chaotic and Stochastic Dynamics Lucas Lin Through the Permutation Spectrum Test Thomas Jefferson High School for Science and Technology In this poster a new test for detecting determinism from [email protected] time series data will be presented. The test involves looking for reoccurring patterns in time series data. The test will Paul So be described and the results of the test applied to several George Mason University model systems and real-world data sets will be presented. The Krasnow Institute The presentation will conclude with a discussion of future [email protected] avenues of research related to the test. Ernest Barreto Christopher W. Kulp George Mason University Dept. of Physics and Astronomy Krasnow Institute [email protected] [email protected]

Luciano Zunino Centro de Investigaciones pticas (CONICET La PP1 Plata-CIC) Shape Coherence and Finite-Time Curvature Evo- DS15 Abstracts 217

lution in Time-Dependent Dynamical Systems Physics Institute - University of So Paulo [email protected] We present finite-time curvature (FTC) as a local propen- sity of curvature elements to change. The FTC simplifies Iber L. Caldas the recent study of shape coherence in nonautonomous dy- Instituto de Fsica, Universidade de So Paulo namical systems. Trough (low) FTC curves indicate shape [email protected] coherent sets. Finding slowly evolving boundary curvature describes slowly changing shapes in otherwise complex non- linear flows, where stretching and folding may dominate. Murilo Baptista FTC troughs are often nearby the popular Finite-Time University of Aberdeen Lyapunov Exponent (FTLE) ridges, but often the FTC [email protected] indicates entirely different regions.

Tian Ma PP1 Department of Mathematics and Computer Science A Biophysical Model for the Role of Network Clarkson University Topology in Regulating a Two-Phase Breathing [email protected] Rhythm Respiration occurs in a two-phase pattern, with alternat- Erik Bollt ing inspiration and expiration. This arises from alternat- Clarkson University ing activity among groups of neurons in the pre-Btzinger [email protected] and Btzinger areas in the brainstem. However, much about the network mechanisms that produce this activity remains PP1 unknown. Using a biophysical computational model to ex- plore different topological structures and their ability to Snaking on Networks: From Local Solutions to generate a two-phase rhythm, we show how modular vs. Turing Patterns random structure of the inhibitory connections affect global The emergence of patterns of activity on complex networks dynamics. with reaction-diffusion dynamics on the nodes is studied. Joshua Mendoza The transition is investigated between the single-node so- Department of Applied Mathematics, University of lutions, studied previously [Wolfrum, Physica D (2012)], Washington and the fully developed global activation states (so called Lewis Hall #202, Box 353925, Seattle, WA 98195-3925 Turing states). Numerical continuation reveals snaking bi- USA furcations connecting different solutions, similar to those [email protected] found in reaction diffusion systems on regular lattice net- work topologies, shedding light on the origin of the mul- tistable “Turing’ patterns reported previously [Nakao & Kameron Decker Harris Mikhailov, Nature 2010]. Department of Applied Mathematics, University of Washington Nick McCullen [email protected] Architecture and Civil Engineering University of Bath Eric Shea-Brown [email protected] University of Washington Department of Applied Mathematics Matthias Wolfrum [email protected] Weierstrass Institute for Applied Analysis and Stochastics [email protected] Jan Ramirez Center for Integrative Brain Research, Seattle Childrens Thomas Wagenknecht [email protected] University of Leeds deceased Tatiana Dashevskiy Center for Integrative Brain Research Seattle Children’s Research Institute PP1 [email protected] Fractal Boundaries in the Parameters Space of De- terministic Dynamical Systems PP1 Nonlinear dynamical systems may exhibit sensitivity to Modeling Effects of Drugs of Abuse on Hiv-Specific small perturbations in their control parameters. Such sen- Antibody Responses sitivity is source of uncertainties on the predictability of tunning parameters that lead these systems to either a Drugs of abuse enhance HIV replication and diminish host chaotic or a periodic behavior. In this work, by quantifying immune responses. Here, we present a dynamical system such uncertainties in different classes of nonlinear systems, model that helps quantify the effects of drugs of abuse on we obtain the exterior dimension of parameters sets that altering HIV-specific antibody responses. Our model is lead the system to chaotic or to periodic behavior. we show consistent with the experimental data from simian immun- that this dimension is fractal, explaining the sensitivity odeficiency virus infection of morphine-addicted macaques. observed in tunning the parameter to those two behaviors. Using our model, we show how altered antibody responses Moreover, we show that this dimension is roughly the same due to drugs of abuse affect steady state viral load and for the classes of investigated systems. CD4 count in HIV-infected drug abusers.

Everton S. Medeiros Jones M. Mutua 218 DS15 Abstracts

University of Missouri - Kansas City (UMKC) affects the spread. In this poster we will use analytical [email protected] methods to derive an expression for TBRF’s fundamental reproductive number R0 as a function of the number of Anil Kumar relapses. University of Missouri - Kansas City [email protected] Cody Palmer University of Montana Naveen K. Vaidya [email protected] Dept of Maths & Stats, University of Missouri - Kansas City Kansas City, Missouri, USA PP1 [email protected] Title Not Available

PP1 Our work builds on Kurebayashi et al. (2013), where they derive a general phase equation for an autonomous Time-Delayed Model of Immune Response in system with a slowly varying parameter. We reproduce Plants their result using the Fredholm alternative, and extend it When studying the dynamics of plant infections, it is essen- to weakly coupled oscillators by deriving an equation for tial to correctly account for detailed mechanisms of plant the interaction function with a slowly varying parameter. immune response. We have developed and analysed a new We test our theory with a lambda-omega system and a mathematical model of plant immune response that takes Traub+adaptation model using stochastic, periodic, and post-transcriptional gene silencing into account. We have quasi-periodic slow parameters. performed analytical and numerical bifurcation analysis to investigate how stability of the steady states depends Youngmin Park on time delays, and also to illustrate different dynamical University of Pittsburgh regimes that can be exhibited by the model. [email protected]

Giannis Neofytou, Konstantin Blyuss University of Sussex PP1 [email protected], [email protected] Stochastic Motion of Bumps in Planar Neural Fields PP1 Analysis and Control of Pre-Extinction Dynamics We analyze the effects of spatiotemporal noise on station- in Stochastic Populations ary pulse solutions (bumps) in neural field equations on planar domains. Fluctuations in neural activity are mod- We consider a stochastic population model where the in- eled as a Langevin equation. Noise causes bumps to wan- trinsic noise causes random switching between metastable der diffusively. We derive effective equations describing the states before the population goes extinct. Switching and bump dynamics as Brownian motion in two-dimensions. extinction times are found using a master equation ap- We also consider weak external inputs that can pin the proach and a WKB approximation. In addition, a proba- bump so that it obeys an Ornstein-Uhlenbeck process with bilistic argument is used to understand the pre-extinction coefficients determined by input shape. cycling dynamics. We also implement a control method to decrease the mean time to extinction. Analytical results Daniel Poll agree well with numerical Monte Carlo simulations. University of Houston Department of Mathematics Garrett Nieddu [email protected] Montclair State University [email protected] Zachary Kilpatrick University of Houston Lora Billings [email protected] Montclair State University Dept. of Mathematical Sciences [email protected] PP1

Eric Forgoston Automatically Proving Periodic Solutions to Poly- Montclair State University nomial ODEs Department of Mathematical Sciences [email protected] Rigorously proving the existence of a solution to ODEs in a neighborhood of a given numerical approximation is of primary importance in order to determine the accuracy of PP1 the numerical approximation. One approach is to use a An Explicit Formula for R0 of Tick-Borne Relaps- functional analytic setting that is well suited to continu- ing Fever ation techniques. We discuss an implementation for peri- odic solutions to general systems of polynomial ODEs. We Tick Borne Relapsing Fever (TBRF) is a disease spread present several examples that serve as test problems for the among mammals by soft bodied ticks in the Western automated algorithm. United States which is characterized by (possibly multiple) relapsing states of fever and muscle aches. There is a nat- Elena Queirolo ural question regarding how the number of relapse states Vrije Universiteit Amsterdam DS15 Abstracts 219

[email protected] non-rigorous numerical simulation of dynamical systems and mathematically sound results. Recently, a rigorous numerical procedure based on Chebyshev-series (a non- PP1 periodic analog of Fourier series) was developed to solve Repulsive Inhibition Promotes Synchrony in Exci- ODEs and BVPs. My research is concerned with extend- tatory Networks of Bursting Neurons ing this method by incorporating domain decomposition. Applications include rigorous computations of connecting We show that the addition of pairwise repulsive inhibition and periodic orbits in the Lorenz-system. to excitatory networks of bursting neurons induces syn- chrony, in contrast to one’s expectations. Through sta- Ray Sheombarsing bility analysis, we reveal the mechanism underlying this VU University Amsterdam purely synergetic phenomenon and demonstrate that it [email protected] originates from the transition between bursting of different types, caused by excitatory-inhibitory synaptic coupling. We also reveal a synergetic interplay of repulsive inhibi- PP1 tion and electrical coupling in synchronization of bursting Central Configurations of Symmetrically Re- networks. stricted Five-Body Problem

Reimbay Reimbayev, Igor Belykh We study the central configuration of a highly symmetric Department of Mathematics and Statistics five-body problem where four of the masses are placed at Georgia State University the vertices of the isosceles trapezoid and the fifth body can [email protected], [email protected] take various positions on the axis of symmetry. We identify regions in the phase space where it is possible to choose pos- itive masses which will make the configuration central. We PP1 propose a global regularization scheme which removes sin- Quasipatterns in Two and Three Dimensions gularities associated with single-binary collisions. Finally we numerically show existence of quasi-periodic orbits in Quasipatterns (patterns with no translation symmetry but the central configuration regions. with rotation symmetry on average) can occur in a vari- ety of systems, including Faraday waves, nonlinear optics, Anoop Sivasankaran polymer micelles and coupled reaction-diffusion systems. Khalifa University of Science Technology and Research This poster will explore how having two interacting wave- Department of Applied Mathematics and Science lengths in the physical system can stabilise quasipatterns [email protected] in two and three dimensions, or can lead to spatio-temporal chaos. Muhammad Shoaib University of Hail, Department of Mathematics Alastair M. Rucklidge Saudi Arabia Department of Applied Mathematics [email protected] University of Leeds [email protected] Abdulrehman Kashif University of Hail, Department of Mathematics PP1 [email protected] Computing Chaotic Transport Properties in a Mixed Phase Space with Periodic Orbits PP1 Chaotic transport can be quantified using periodic orbits, Finite Time Diagnostics and Transport Barriers in but difficulties arise in a mixed Hamiltonian phase space. Non Twist Systems Homotopic Lobe Dynamics uses topological forcing by in- tersections of stable and unstable manifolds of anchor or- Internal transport barriers that appear in Hamiltonian dy- bits to find periodic orbits in such a space. We compute namical systems have been proposed as an explanation for decay rates for the H´enon map in a variety of parameter the cessation or reduction of transport in physical systems regimes. In a hyperbolic plateau, periodic orbit continua- at describe fluids and plasmas. These barriers may have tion is used to accurately compute the decay rate for the various physical or dynamical origins, yet they can and entire interval. have been used to control experiments and sometimes to improve desired confinement of trajectories. We use the Sulimon Sattari so-called standard nontwist map, a paradigmatic example University of California, Merced of non twist systems, to analyze the parameter dependence School of Natural Sciences of the transport through a broken barrier. On varying a [email protected] proper control parameter, we identify the onset of struc- tures with high stickiness that give rise to an effective bar- Kevin A. Mitchell riers. We use the finite-time rotation number to identify University of California, Merced transport barriers that separate different regions of stick- Physics iness. The identified barriers are comparable to those ob- [email protected] tained by using finite-time Lyapunov exponents. Jose D. Szezech Jr PP1 University State of Ponta Grossa Rigorous Computations for BVPs with Chebyshev- [email protected] series Ibere L. Caldas The main goal of my research is to bridge the gap between Institute of Physics 220 DS15 Abstracts

University of Sao Paulo the stability of different symmetric cluster states, and ap- [email protected] plied the results to a network of six globally coupled Morris- Lecar oscillators with synaptic coupling. Furthermore, we Sergio R. Lopes compare the phase model results to bifurcation studies of Department of Physics the full model. Federal University of Parana lopes@fisica.ufpr.br Zhen Wang University of Waterloo Ricardo L. Viana [email protected] Departmento de Fisica Federal University of Parana viana@fisica.ufpr.br PP1 Efficient Design of Navigable Networks Philip Morrison Physics Department Navigation is a dynamic process where individual agents University of Texas at Austin try to reach targets given limited knowledge. In a net- [email protected] work of agents, we term a successive gradient-like naviga- tion path to the target as a greedy path, and show that (interestingly) it violates many known properties of usual PP1 network paths such as symmetry and transitivity even for Robust Pulse Generators in An Excitable Medium undirected networks. Despite these complications, we are able to design an efficient scheme that allows every network We study a spontaneous pulse-generating mechanism in an to be navigable. excitable medium with jump-type heterogeneity. We in- vestigate the conditions for the onset of robust-type pulse B.M. Shandeepa D. Wickramasinghe generators, and then we show the global bifurcation struc- Clarkson University, 8 Clarkson avenue, Potsdam,Ny ture of heterogeneity-induced patterns, including the ho- [email protected] moclinic orbits that are homoclinic to a special type of heterogeneity-induced ordered pattern. These numerical Jie Sun approaches assist us in identifying a candidate for the or- Clarkson University ganizing center as a codimension-two gluing bifurcation. [email protected]

Takashi Teramoto PP1 Asahikawa Medical University Instability of Certain Equilibrium Solutions of the [email protected] Euler Fluid Equations

We look at the stability of the family of stationary solutions PP1 cos(mx + ny) of the Euler Equations on a toroidal domain. Dynamical Building Blocks in Turbulent Two- We use a Poisson structure preserving truncation described Dimensional Channel Flow by Zeitlin [1991] to turn the problem into a finite-mode system, and a splitting into subsystems described by Li Although the classical sweep-ejection cycles cannot be self- [2000]. We show that for many m and n these stationary sustaining itself, two-dimensional channel flows keep them solutions are unstable. regenerating for a quite long time. The relation between localized coherent structures and their collective dynamics Joachim Worthington is investigated numerically focusing on a turbulent-laminar University of Sydney, Australia interface. The existence of interfaces reduces the complex- [email protected] ity of the collective dynamics arising around them. We use the damping filter technique to simulate a laminar- turbulent interface in a periodic box. Holger R. Dullin University of Sydney Toshiki Teramura School of Mathematics and Statistics Department of Physics and Astronomy, [email protected] Graduate School of Science, Kyoto University, Japan [email protected] Robby Marangell University of Sydney Sadayoshi Toh [email protected] Graduate School of Science, Kyoto University, Japan [email protected] PP1 A Symbolic Method in Chua’s Circuit PP1 Phase Models and Oscillators with Time Delayed A symbolic method is introduced in a three-dimensional All-to-All Coupling Chua’s circuit with a smooth cubic nonlinearity. The new method is able to reveal thousands of homoclinic bifurca- We consider a system modeling a network of globally de- tion curves in a bi-parametric plane with a small amount of layed coupled identical oscillators. Assuming weak cou- computational cost. Co-dimension two points, t-points and pling, we reduce the system to a phase model where the close homoclinc curves are detected as well. Based on the delay acts as a phase shift. We show how the delay affects bi-parametric plots of the Chua’s circuit, chaotic structure DS15 Abstracts 221

of the Chua’s circuit is studied. [email protected]

Tingli Xing Georgia State University PP2 USA Intermittent Synchronization/desynchronization [email protected] in Population Dynamics

Andrey Shilnikov Synchronous dynamics of spatially distinct oscillating pop- Neuroscience Institute and Department of Mathematics ulations is a well-known phenomenon in ecology. Mathe- Georgia State University matical modeling of this phenomenon has been largely fo- [email protected] cused on the synchronization conditions and the properties of synchronized dynamics. Yet the synchrony in the real populations is not necessary strong and therefore exhibit PP1 intervals of uncorrelated, desynchronized dynamics. We Interactions of Solitary Modes in Models of Bacte- explore the properties of these time-intervals and discuss rial Chemotaxis potential advantages and disadvantages of short numerous desynchronization intervals vs. few long desynchronization We study the interaction of two colliding bacterial popula- intervals. tions in a one-dimensional nutrient gradient. The outcome Sungwoo Ahn of such collisions varies. For example, upon collision, two Indiana University Purdue University Indianapolis populations of E. coli will either mix together to become [email protected] one indistinguishable population or deflect off and move away from one another. We use a Keller-Segel model of bacterial chemotaxis to determine mechanisms by which Leonid Rubchinsky each observed outcome may occur and make experimental Department of Mathematical Sciences predictions about the behavior following a collision. Indiana University Purdue University Indianapolis [email protected] Glenn S. Young University of Pittsburgh Department of Mathematics PP2 [email protected] Parabolic Bursting in Inhibitory Neural Circuits

Hanna Salman We study the rhythmogenesis of network bursting emerging University of Pittsburgh in inhibitory motifs comprised of tonic spiking interneu- Department of Physics and Astronomy rons described by an adopted Plant model.Such motifs are [email protected] the building blocks in larger neural networks, including the central pattern generator controlling swim locomotion of sea slug Melibe leonine. Bard Ermentrout University of Pittsburgh Deniz Alacam Department of Mathematics Georgia State University [email protected] Mathematics Department [email protected] Jonathan Rubin University of Pittsburgh Andrey Shilnikov Pittsburgh, PA Neuroscience Institute and Department of Mathematics [email protected] Georgia State University [email protected] PP1 The Spread of Activity with Refractory Periods PP2 over Directed Networks An Accurate Computation of the Tangent Map for Computation of Lagrangian Coherent Structures We study propagation of activity in a discrete time dynami- cal system on several directed network topologies. At each The tangent map (flow map gradient) is often used in dy- time step, active nodes send the signal onward through namical systems for computation of Lagrangian coherent their outgoing connections, and fall into a refractory pe- structures. In more sophisticated methods it is important riod. In particular, we investigate the number and length to recover the complete spectrum of this operator, as well of attractors (node sequences that can sustain activity in- as the eigenvectors. Traditional methods to compute the definitely) and transients on networks of varying topologies tangent map using finite differencing often fail in accurately including random, small-world, scale-free. computing these quantities. Due to nonlinear effects of the flow, perturbations of trajectories mapped forward by the Daniel R. Zavitz tangent map may grow excessively and they collapse on University of Utah the dominant eigenvector of the map. We describe alter- Department of Mathematics native techniques to overcome these issues. Both continu- [email protected] ous or discrete singular value decompositions with efficient implementations are used to automatically carry out com- Alla Borisyuk putation of finite time Lyapunov exponents and directions. University of Utah Results on sum of Lyapunov exponents for divergent free Dept of Mathematics flow, as well as sensitivity to integration time are compared 222 DS15 Abstracts

in contrast to previous methods. Nicholas Tufillaro Oregon State University Siavash Ameli, Shawn Shadden [email protected] University of California, Berkeley [email protected], [email protected] Jie Sun Clarkson University PP2 [email protected] Nonlinear Dynamics in Coupled Semiconductor Laser Network Implementations PP2 Coupled semiconductor lasers subject to optical injection Phase Response Analysis of the Circadian Clock in and/or feedback are known to exhibit complex dynamics Neurospora Crassa in their emitted output. Current implementations usually Circadian rhythm is crucial in maintaining an organism’s employ only a few lasers in order to map the regimes of the daily routine. We present a model which accurately sim- exhibited dynamics. In the present work, a large-scale net- ulates the molecular components governing the circadian work of coupled semiconductor lasers is built experimen- clock of the model organism, Neurospora crassa.Environ- tally, including up to 24 laser devices. Rich dynamics are mental cues such as light perturb the phase of the circadian recorded, depending on the conditions of coupling strength oscillator, a phenomenon generally measured with a phase and time delays among the laser nodes. response curve (PRC). Our model advocates that Neu- Apostolos Argyris, Michail Bourmpos, Alexandros rospora’s phase response to light is primarily regulated by Fragkos, Dimitris Syvridis the degradation of the clock protein White Collar-1 (WC- Department of Informatics and Telecommunications 1). National & Kapodistrian University Of Athens Jacob Bellman [email protected], [email protected], alx [email protected], University of Cincinnati [email protected] [email protected]

PP2 PP2 Symplectic Maps with Reversed Current in a Toka- maks Time Series Based Prediction of Extreme Events in High-Dimensional Excitable Systems Plasmas are confined in tokamaks by magnetic field lines. We derive a bidimensional conservative map which de- We investigate extreme events in a high-dimensional deter- scribes these lines considering a non-monotonic profile of ministic system: a network of FitzHugh-Nagumo units. We safety factor with reversed current density, first in equilib- present a data-driven approach to predict extreme events rium [C. Martins et al., Analytical solutions for Tokamak which is only based on the time series of some observables equilibria with reversed toroidal current, PoP 18(2011)], and on the coupling topology of the network. By itera- and then we will apply a perturbation (ergodic magnetic tive predictions, we are able to forecast the onset of an limiter). We will investigate island chains, chaos and par- extreme event as well as the propagation and extinction of ticle transport. excitation, i.e. the full life-cycle of an extreme event. Bruno Bartoloni Stephan Bialonski University of Sao Paulo Max-Planck-Institute for the Physics of Complex Systems Institute of Physics [email protected] [email protected] Gerrit Ansmann Ibere L. Caldas Department of Epileptology Institute of Physics University of Bonn, Germany University of Sao Paulo [email protected] [email protected] Holger Kantz Max-Planck-Institute for the Physics of Complex Systems PP2 [email protected] Analysis of Spatiotemporal Dynamical Systems from Multi-Attribute Satellite Images PP2 We deduce and then analyze oceanic fluid systems by re- Slow-fast Analysis of Earthquake Faulting mote sensing from satellite images. Time varying vec- tor fields are computed from the nonautonomous system We consider a rate and state dependent friction law to by temporal intensity changes of observed product move- study earthquake fault dynamics. We show that the sys- ments. To emphasize prior assumed physics, an objective tem has an embedded slow-fast structure. Using techniques function and consequent calculus of variations follows. As from geometric singular perturbation theory and centre an important initial task, we show how to remove sensor- manifold theory we perform an analytical investigation of data biased of stripes from images by developing a new the problem. approach in terms of a nonisotropic total variation denois- ing. Elena Bossolini Ph.D. student Ranil Basnayake, Erik Bollt DTU Compute, Institute for Mathematics and Computer Clarkson University Science [email protected], [email protected] [email protected] DS15 Abstracts 223

Kristian Uldall Kristiansen, Morten Brøns Temporary Immunity Technical University of Denmark Department of Applied Mathematics and Computer In an SIRS compartment model for a disease we consider Science the effect of different probability distributions for remain- [email protected], [email protected] ing immune. We show that to first approximation the first three moments of the corresponding probability densities are sufficient to well describe oscillatory solutions corre- PP2 sponding to recurrent epidemics. We consider six differ- Quasicycles in the Stochastic Hybrid Morris-Lecar ent distributions and show that by tuning their parame- Neural Model ters such that they have equivalent moments that they all exhibit equivalent dynamical behavior. Intrinsic noise from the stochastic nature of voltage-gated ion channels affects a neuron’s ability to produce sub- Thomas W. Carr threshold oscillations and respond to weak periodic stim- Southern Methodist University uli. While it is known that stochastic models can produce Department of Mathematics oscillations in regimes where the deterministic model has [email protected] only a stable fixed point, little work has explored these connections to channel noise. Using a stochastic hybrid Morris-Lecar model, we use various approximation schemes PP2 to derive a stochastic differential equation, then derive the A Novel Speech-Based Diagnostic Test for Parkin- power spectrum and quantify how oscillations are affected sons Disease Integrating Machine Learning with by channel noise. Web and Mobile Application Development for Cloud Deployment Heather A. Brooks University of Utah Parkinson’s disease remains one of the most poorly diag- [email protected] nosed neurological conditions despite the critical need of early diagnosis for effective management and treatment. Paul C. Bressloff This work presents a new method of diagnosing Parkin- University of Utah son’s disease and accompanying scalable web and mobile Department of Mathematics applications towards the goal of employing this diagnostic bressloff@math.utah.edu test to the cloud. This method provides a more simple, inexpensive, and rapid approach than traditional diagno- sis strategies by requiring the patient to only speak into PP2 a microphone attached to their computer or mobile device Computation of Normally Hyperbolic Invariant before providing a diagnosis within seconds. This work em- Manifolds ploys speech processing algorithms, an artificial neural net- work for machine learning, and an application framework In this poster we explain a method for the computation with a user-friendly interface that packages the speech test of normally hyperbolic invariant manifolds (NHIM) in dis- and diagnosis results for easy access by patients and physi- crete dynamical systems. The method is based in finding cians. The diagnosis test developed was tested with actual a parameterization for the manifold formulating a func- patient data and was shown to be highly accurate. tional equation. We solve the invariance equation using a Newton-like method taking advantage of the dynamics Pooja Chandrashekar and the geometry of the invariant manifold and its invari- Thomas Jefferson High School for Science and Technology ant bundles. Particularly, we present two different kind [email protected] of methods to compute normally hyperbolic invariant tori, NHIT. The first method is based on a KAM-like theorem in a-posteriori format for the existence of quasi-periodic PP2 invariant tori, which provides us an efficient algorithm for An Agent-Based Model for mRNA Localization in computing NHIT, by adjusting parameters of the family. Frog Oocytes The second method allows us to compute a NHIT and its internal dynamics, which is a-priori unknown. We imple- During early development of Xenopus laevis oocytes, ment both methods to continue the invariant tori with re- mRNA moves from the nucleus to the periphery. We use spect to parameters, and to explore different mechanisms an agent-based model to study the movement of mRNA by of breakdown. molecular motor transport and diffusion. Our results sug- gest that an anchoring mechanism is required to achieve the Marta Canadell observed localization of mRNA: simulations indicate that Universitat de Barcelona anchoring of a particular motor-mRNA complex may be [email protected] sufficient for relocation and that binding between different molecular motors may contribute to transport. Alex Haro Dept. of Mat. Apl. i Analisi Veronica M. Ciocanel Univ. de Barcelona Brown University [email protected] Brown University veronica [email protected]

PP2 Bjorn Sandstede Equivalent Probability Density Moments Deter- Division of Applied Mathematics mine Equivalent Epidemics in An Sirs Model with Brown University 224 DS15 Abstracts

bjorn [email protected] Prey Swarms

PP2 Real-world predator-prey interactions often involve a predator chasing a flock of prey. We examined a dynamical Effects of Stochastic Gap-Junctional Coupling in systems model of predator-prey interactions, governed by Cardiac Cells and Tissue isometric interaction kernels incorporating classical swarm- ing for the prey. Since many parameter values lead to the Action potentials propagate in cardiac tissue in part predator splitting the swarm into smaller, unevenly-sized through gap junctions. Gap-junction gating dynamics are groups, we investigate the effects of heterogeneity among functions of both gap-junctional voltage and time and also predator-prey interactions in small swarms. We show that are stochastic in nature. We derive a system of stochas- a variety of behaviors, including oscillations, are possible tic differential equations to model these gating dynamics in the small swarm case. within the context of the Luo-Rudy-1 description of ionic currents. We perform simulations on a 1D cable and show the effects of stochastic gating on action potential propaga- Jeff Dunworth tion. Results on conduction block, action potential prop- University of Pittsburgh agation speed and gap junctional resistance will be pre- [email protected] sented. Bard Ermentrout William Consagra University of Pittsburgh Rochester Institute of Technology Department of Mathematics School of Mathematical Sciences [email protected] [email protected]

PP2 PP2 Maximizing Plant Fitness Under Herbivore Attack Bacterial Disinfection with the Presence of Persis- When attacked by insect herbivores, plants emit volatile ters chemicals. These chemicals are known to induce local de- fenses, prime neighboring plants for defense, and attract Many important diseases like Tuberculosis are caused by predators and parasitoids to combat the herbivores, but biofilms.Among the bacteria within a biofilm, persisters these chemical defenses are coupled with fitness costs. We are a subpopulation which are tolerant to antibiotics and examine the interactions between the model plant, gold- knowing more about them is very critical and helpful. In enrod, and one of its insect herbivores, Trirhabda virgata, this poster we will look at the behavior of the bacteria in order to draw conclusions about what defense strategies with three phases: Susceptible, Stationary and Persisters, will maximize a goldenrods fitness. and we will show that considering the third phase gives us more accurate results comparing to the previous studies Karen M. Cumings, Peter R. Kramer with just Susceptible and Persisters and this new model Rensselaer Polytechnic Institute matches the experimental results better. Department of Mathematical Sciences [email protected], [email protected] Sepideh Ebadi Bradford C. Lister Florida State University Rensselaer Polytechnic Institute [email protected] Department of Biological Sciences [email protected] PP2

PP2 Chaotic Mixing in a Curved Channel with Slip Sur- The Derivation of Mass Action Laws: Issues and faces Questions In this work, we show that laminar flow in a planar curved There are well-trodden paths that enable one to pass channel can generate chaotic trajectories, if the top and from stochastic individual-based models to deterministic bottom walls are alternately patterned with slip surfaces. population-level models. I will point out a few issues that Existing micro-mixers based on flow through curved sec- arise along the way: these make the journey slightly more tions, have either complex 3D geometries, or are effective involved and interesting than one might expect. only at relatively high Reynolds numbers [Stremler, Phil. Jonathan Dawes Trans. A., 362, 10191036]. Using slip surfaces, we over- University of Bath come both these limitations, while simultaneously reducing [email protected] viscous drag on the fluid.

Max O. Souza Piyush Garg Departamento de Matem´atica Aplicada Department of Chemical Engineering Universidade Federal Fluminense Indian Institute of Technology Roorkee [email protected]ff.br [email protected]

Jason R. Picardo, Subramaniam Pushpavanam PP2 Department of Chemical Engineering Heterogeneity and Oscillations in Small Predator- Indian Institute of Technology Madras DS15 Abstracts 225

[email protected], [email protected] Complex Systems Group University of Pennsylvania [email protected] PP2 Feasibility of Binding Heteroclinic Networks Fabio Pasqualetti Department of Mechanical Engineering Many neuronal systems exhibit multi-sensory dynamics. University of California, Riverside, CA Multisensory integration is a process by which information [email protected] from different sensory systems is combined to influence per- ception, decisions, and overt behavior. In this context, the Matthew Ceislak, Scott Grafton different sensory systems, such as sight, sound, smell, taste Department of Psychological and Brain Sciences and so on, are called sensory modalities. In each modality, University of California, Santa Barbara, CA there are cognitive modes which are large collections of neu- [email protected], [email protected] rons firing at the same time in synchrony in a functional network. In order to explain the sequential mental pro- cesses in the brain, we study a heteroclinic binding model Danielle S. Bassett where active brain modes form different modalities which Department of Electrical & Systems Engineering, are processed in parallel. Under certain assumptions, the University of Pennsylvania, Philadelphia, PA existence of the so-called multimodality heteroclinic net- [email protected] work was established. we prove that for each collection of successive heteroclinic orbits inside the network, there is PP2 an open set of initial points such that the trajectory going through each of them follows the prescribed collection of Compressive Sensing with Exactly Solvable Chaos successive heteroclinic orbits and stays in a small neigh- Recent advances in sampling theory allow the reconstruc- borhood of it. We also show that the symbolic complexity tion of signals sampled at sub-Nyquist rates. Compres- function of the system restricted to this neighborhood is sive sensing operates under the premise that signal acqui- a polynomial of degree L − 1whereL is the number of sition and data compression can be carried out simultane- modalities. ously. Building on recent work in chaotic communications, Xue Gong a compressive negative Beta encoder/decoder is presented Ohio University that represents data in an irrational radix. Using an exact [email protected] chaotic oscillator and pulsed linear filter, a complete A/D and D/A architecture based on chaotic dynamics can be built in hardware. Valentin Afraimovich Universidad Aut´onoma de San Luis Potos Sidni Hale, Anthony DiPofi, Bradley Kimbrell S.L.P., M´exico Radix Phi [email protected] [email protected], [email protected], [email protected] PP2 Dynamic Square Patterns in 2D Neural Fields PP2 Identifying the Role of Store-Operated Calcium We present analysis and simulation of periodic solutions 2 Channels in Astrocytes Via An Open-Cell Model near D4xT symmetric Hopf bifurcations in two different neural field models. The first model consists of a scalar in- Astrocytes are the most common glial cells in the brain, tegral equation that incorporates finite transmission speed communicating via calcium transients, and possibly mod- through spatiotemporal delays. The second model incorpo- ulating neuronal signals. However, these calcium dynamics rates finite transmission speed using a telegraph equation differ between in vivo and in vitro. We suggest a new open- (ie. a hyperbolic PDE), but also includes local ion channel cell mathematical model that allows us to vary parameters dynamics and 2 interacting populations of neurons. such as cell volume and flux through calcium channels not easily accessible by experimentalists. Our results support Kevin R. Green, Lennaert van Veen the idea that store-operated calcium channels play a key UOIT role, and suggest realistic, follow-up experiments. [email protected], [email protected] Gregory A. Handy University of Utah Mathematics Department PP2 [email protected] Controllability of Brain Networks Alla Borisyuk Cognitive function is driven by dynamic interactions be- University of Utah tween large-scale neural networks, enabling behavior. We Dept of Mathematics use control theory to offer a mechanistic explanation for [email protected] how the brain moves among cognitive states. Our re- sults suggest that densely connected areas facilitate the movement of the brain to easily-reachable states. Weakly Marsa Taheri connected areas facilitate the movement of the brain to University of Utah difficult-to-reach states. Areas located on the boundary Department of Bioengineering between network communities facilitate the integration or [email protected] segregation of diverse cognitive systems. John White Shi Gu department of Bioengineering 226 DS15 Abstracts

The University of Utha [email protected] [email protected]

PP2 PP2 Windows of Opportunity: Synchronization in On- Behavioral Dynamics and STD Transmission Off Stochastic Networks

Many mathematical models of infectious disease transmis- We study dynamical networks whose topology and intrin- sion represent contact patterns using fixed rate parameters. sic parameters stochastically change, on a time scale that However, individual contact and protective behaviors are ranges from fast to slow. When switching is fast, the likely to respond elastically to disease outbreaks. We use stochastic network synchronizes as long as synchronization the replicator-mutator equations from evolutionary game in the averaged network, becomes stable. We prove global theory to couple the dynamics of protective sexual behav- stability of synchronization in the fast switching limit. Be- ior to a simple SIS compartmental model. Our combined yond fast switching, we reveal unexpected windows of in- model demonstrates a shift in effective contact reduction termediate switching frequencies in which synchronization behavior over the course of the outbreak, driven by the becomes stable despite the instability of the averaged/fast- behavioral-disease interaction dynamics. switching network.

Michael A. Hayashi Russell Jeter University of Michigan School of Public Health Georgia State University [email protected] [email protected]

Marisa Eisenberg Igor Belykh University of Michigan Department of Mathematics and Statistics [email protected] Georgia State University [email protected]

PP2 Master Stability Functions for the Fixed Point So- PP2 lution of Synchronized Identical Systems with Lin- Two-Theta Neuron: Phase Models for Bursting ear Delay-Coupling and a Single Constant Delay Networks

This poster presents master stability functions for the fixed We continue our reduction approach to study bursting out- point solution of any network of synchronized identical sys- comes of central pattern generators using coupled two- tems with linear delay-coupling and a single constant delay. theta phase models. We examine configurations of 3-cell The connection between these master stability functions CPGs with inhibitory, excitatory and electrical synapses, and amplitude death islands is also provided using numer- and model and compare with corresponding real-world ex- ical simulations of small oscillator networks with identical emplary networks. Occurrence, robustness and transfor- chaotic node dynamics. mations of CPG outcomes are studied using 2D return maps, stable fixed points and invariant circles correspond Stanley R. Huddy, Jie Sun to bursting patterns with fixed and varying phase lags. Clarkson University [email protected], [email protected] Aaron Kelley GSU [email protected] PP2 Rigorous Numerics for Analytic Solutions of Differ- ential Equations: The Radii Polynomial Approach PP2 A mathematical model for adaptive crawling loco- The radii polynomial method has been used for validating motion numerical approximations to Ck periodic solutions of dif- ferential equations. This paper discusses the extension (via Crawling with locomotory wave is a fundamental method weighted Fourier sequence spaces) of the method to solu- of biological locomotion in invertebrate including limbless tions in the analytic category, which often leads to better and legged animals. We conducted observations of crawling bounds and the possibility of continuation of the solution locomotion in largely different conditions. In particular, it as a manifold in parameter space. It then details two exam- was found that centipedes can variously change their leg- ples in which our numerics have led us to computer-assisted density waves which represent spatio-temporal coordina- proof of solutions. tion pattern of ground friction. Here, we present a simple mechano-mathematical model for crawler so that it pro- Allan R. Hungria vides observed mode transition depending on the external University of Delaware / internal conditions. [email protected] Shigeru Kuroda Jean-Philippe Lessard Research Institute for Electronic Science, Universit´eLaval Hokkaido university [email protected] [email protected]

Jason Mireles-James Toshiyuki Nakagaki Departement of Mathematics Rearch Institute for Electronical Science Florida Atlantic University Hokkaido University DS15 Abstracts 227

[email protected] Paul C. Bressloff University of Utah Department of Mathematics PP2 bressloff@math.utah.edu Canard-Mediated Dynamics in a Phantom Burster

We present canard-mediated dynamics arising in a phan- PP2 tom burster, formed by a multiple timescale model com- Modelocking in Chaotic Advection-Reaction- posed of FitzHugh-Nagumo systems, which represents an Diffusion Systems alternating pulse and surge pattern in a neuro-secretory context. So far, global and local features of the model Systems undergoing chaotic advection-reaction-diffusion have been studied in the context of slow-fast dynamics and dynamics have rich topological structures that define the mixed-mode oscillations where folded singularities and as- front propagation. Here we use burning invariant manifolds sociated canard trajectories have a particular importance. (BIMs) to provide a theoretical framework that explains Here, we study the effect of the folded singularities in slow- modelocking as observed experimentally and in numerical fast transitions. simulations. The existence of a relative periodic orbit and the shape of the BIM determine the type of modelock- Elif K¨oksal Ers¨oz, Mathieu Desroches, Maciej Krupa, ing. Using this technique we find higher order modelock- Fr´ed´erique Cle´ement ing types and discuss the switching of modelocking types INRIA Paris-Rocquencourt observed in experiments. [email protected], [email protected], ma- [email protected], [email protected] Rory A. Locke UC-Merced [email protected] PP2 Effective Dispersion Relation of the Nonlinear John R. Mahoney Schr¨odinger Equation University of California, Merced [email protected] The linear part of the Nonlinear Schr¨odinger Equation 2 (NLS) (iqt = qxx) has dispersion relation ω = k .Wedon’t Kevin A. Mitchell necessarily expect solutions to the NLS to behave nicely or University of California, Merced have any kind of effective dispersion relation, since we ex- Physics pect nonlinear waves to be strongly coupled and not sinu- [email protected] soidal in time. However, I have seen that solutions to the NLS are actually weakly coupled and are often nearly si- nusoidal in time with a dominant frequency. In fact, when PP2 I look at long-time average of either a solution with many Effect of Multi-Species Mass Emergence on Biodi- solitons or with many unstable modes, the power spec- versity tral density does indicate a quadratic dispersion relation that has been shifted by a constant proportional to the 2 Mass emergences are a regular occurrence in rivers and amplitude of the initial condition: ω = k − 2A where streams. Many aquatic insects depend on safety in num- qˆ(k,0)2 A = 2π . I will show a number of plots confirming bers to escape the water and reproduce. This strategy this. not only allows individual species to enhance reproductive success by reducing predation rates, but also creates op- Katelyn J. Leisman, Gregor KovaCiˇ Cˇ portunities for scarcer species that synchronize their emer- Rensselaer Polytechnic Institute gence with more prevalent species. We construct a heuris- [email protected], [email protected] tic model to study inherent protections afforded by biodi- versity and consider implications for repopulation efforts David Cai in pollution-impacted systems. New York University Courant institute James E. McClure [email protected] Advanced Research Computing Virginia Tech [email protected] PP2 Mathematical Model of Bidirectional Vesicle Nicole Abaid Transport and Sporadic Capture in Axons Virginia Polytechnic Institute and State University [email protected] We model the transport of vesicles along an axon using an advection-diffusion equation which includes vesicle degra- dation and sporadic capture by presynaptic targets. Our PP2 model shows that the steady state concentration of vesicles A B Cell Receptor Signaling Model and Dynamic distributed along the axon does not decay exponentially Origins of Cell Response in space for some parameter values. We also study how heterogeneity in the distribution of targets can enhance The kinase Syk is imperative for the intricate signaling cargo delivery by performing a multi-scale homogenization events that occur in B cells, events which lead to cellular in space. responses when antigens bind to B cell receptors (BCRs). We have constructed a deterministic model for BCR signal- Ethan Levien ing centered around Syk. After tuning feedbacks between University of Utah key kinases and phosphatases, we demonstrated qualitative [email protected],edu agreement between the model and dose response data from 228 DS15 Abstracts

literature. We investigate the role of positive and negative [email protected], [email protected] feedbacks in determining cell response.

Reginald Mcgee PP2 Purdue University Capacity for Learning the Shape of Arena in the [email protected] Single-Celled Swimmer, Viewed from Slow Dynam- ics of Membrane Potential.

We have studied for some years the learning capacity for PP2 time and space in unicellular organisms. Here we present Stability of Morphodynamic Equilibria in Tidal that protozoan ciliates, Paramecium and Tetrahymena, Basins show the swimming trajectory adaptive to the shape (e.g. capillary and droplet) of swimming arena in which they experienced just before. As the swimming activity is reg- Interesting bed patterns are observed in the tidal basins ulated by membrane potential in the ciliates, a possible of, for example, the Wadden Sea along the Dutch, Ger- mechanism is considered according to the equations of man and Danish coast. To get a better understanding of Hodgkin-Huxley type with the additional slower variable. these phenomena, a morphodynamic model has been con- structed. The goal is to find the morphodynamic equilibria Toshiyuki Nakagaki and their stability, and to investigate their sensitivity to Rearch Institute for Electronical Science parameter variations. Therefore, the equations have been Hokkaido University scaled and asymptotically analysed. Using finite element [email protected] method and continuation techniques, the equilibrium of the bed has been determined. Itsuki Kunita Hokkaido University Corine J. Meerman [email protected] Leiden University Mathematical Institute Tatsuya Yamaguchi [email protected] Kyushu University tatsuya [email protected] Vivi Rottsch¨afer Department of Mathematics Masakazu Akiyama Leiden University Hokkaido University [email protected] [email protected]

Henk Schuttelaars Atsushi Tero Delft Institute of Applied Mathematics Kyushu University Delft University of Technology [email protected] [email protected] Shigeru Kuroda Research Institute for Electronic Science, PP2 Hokkaido university Frequency-Dependent Left-Right Coordination in [email protected] Locomotor Pattern Generation Kaito Ooki Coordination between left and right activities in the spinal Hokkaido University cord during locomotion is controlled by commissural in- [email protected] terneurons (CINs). Several types have been genetically identified including both excitatory (VOV) and inhibitory PP2 (V0D). Genetic elimination of these CINs caused switch- ing from a normal left-right alternation to a left-right syn- Co-Dimension Two Bifurcations in Piecewise- chronized pattern. Ablation of V0D neurons resulted in Smooth Continuous Dynamical Systems a lack of left-right alternation at low locomotor frequen- The mean-field equations for a network of type I neurons is cies, whereas selective ablation of V0V CINs switched the a piecewise-smooth continuous (PWSC) system of ordinary motor output to a left-right synchronized pattern at high differential equations. This system displays two prominent frequencies. We developed a model of neural circuits con- co-dimension two non-smooth bifurcations involving colli- sisting of four pacemaker neurons, left and right flexors sions of a saddle-node equilibrium with a switching man- and extensors, interacting via V0D and V0V commissural ifold, and a Hopf equilibrium with a switching manifold. pathways. The model reproduced all experimentally iden- These bifurcations are analytically resolved for the mean- tified regimes in the corresponding frequency ranges. We field system in full detail. The genericity of these bifur- qualitatively analyzed the behavior of this network in the cations for an arbitrary PWSC system is also discussed. above regimes and transitions between them.

Yaroslav Molkov Wilten Nicola Indiana University - Purdue University Indianapolis University of Waterloo [email protected] [email protected]

Bartholomew Bacak, Ilya A. Rybak Sue Ann Campbell Drexel University College of Medicine University of Waterloo DS15 Abstracts 229

Dept of Applied Mathematics Patrick Underhill [email protected] Rensselaer Polytechnic Institute [email protected]

PP2 Analysis of Malaria Transmission Dynamics with PP2 Saturated Incidence Consensus and Synchronization over Biologically- Inspired Networks: From Collaboration to Antag- Mathematical model for malaria transmission in a two- onism interacting population with saturated incidence was for- mulated and robustly analysed. The model was shown to The vast majority of work on consensus and synchroniza- exhibit a subcritical bifurcation whenever a unique thresh- tion of coupled dynamical systems considers their interac- old, R0, increases through unity. However, under specific tions to be collaborative. In our present work, we study conditions, globally asymptotically stable malaria-free and two different networks representing more realistic scenar- endemic equilibria were established at R0 < 1andR0 > 1 ios; one consists of dynamic leaders in a collaborative net- respectively. Further, sensitivity analysis and simulations work and another consists of agonistic and antagonistic in- were performed to examine the effects of some parameters teractions. We establish closed form results for the rate of on the model. convergence to consensus for both the cases and conditions for stochastic synchronization in the second case. Samson Olaniyi Department of Pure and Applied Mathematics Subhradeep Roy, Nicole Abaid Ladoke Akintola University of Technology, Ogbomoso Virginia Polytechnic Institute and State University [email protected] [email protected], [email protected]

PP2 PP2 Temporally Periodic Neural Responses from Spa- Oscillatory Shear Flow Influence on the Two Point tially Periodic Stimuli Vortex Dynamics Certain static spatial visual patterns induce temporally varying neural responses, such as in pattern-sensitive Bounded and unbounded quasi-periodic dynamics of two epilepsy and some visual illusions. These temporal re- point vortices of unequal strengths embedded in an oscilla- sponses are often strong only in a very narrow spatial tory shear flow with rotation is addressed with an emphasis frequency band and nonexistent at other spatial frequen- on their impact on passive tracer transport. All the sets of cies. We present a spatially distributed neural field model the vortex signs are shown to induce qualitatively divergent that captures this resonant behavior in simulations, and transport patterns. Regions enduring effective stretching, demonstrate analytically this strong sensitivity to the spa- and consequently prone to intense mixing are identified by tial wavelength with a perturbation calculation near the means of finite-time Lyapunov exponents. instability. Evgeny Ryzhov Jason E. Pina V.I. Ilichev Pacific Oceanological Institute University of Pittsburgh Department of Mathematics [email protected] [email protected] Konstantin Koshel Bard Ermentrout V.I. Ilichev Pacific Oceanological Institute University of Pittsburgh Far Eastern Federal University Department of Mathematics [email protected] [email protected] PP2 PP2 Waveaction Spectra for Fully Nonlinear MMT Using a Stochastic Field Theory to Understand Model Collective Behavior of Swimming Microorganisms We investigate a version of the Majda-McLaughlin-Tabak Large groups of active particles can show collective behav- model of dispersive wave turbulence where the linear term ior and enhanced fluctuations, but mean field theories to in the time derivative is removed. We are interested in understand them ignore fluctuations. We have extended the long-time average of the distribution of waveaction these field theories to include stochastic fluxes and have throughout the system as a function of wavenumber. We quantified the dynamics in terms of enhanced diffusion consider driven-damped and undriven, undamped cases of and mixing and number fluctuations. We have also com- the model. Our theoretical predictions, which include self- pared with results with the mean field theory and discrete similarity arguments and statistical mechanical methods, particle-based simulations. are found to agree with time dynamics simulations.

Yuzhou Qian Michael Schwarz Rensselaer Polytechnic Institute Rensselaer Polytechnic Institute [email protected] [email protected]

Peter R. Kramer Gregor Kovacic Rensselaer Polytechnic Institute Rensselaer Polytechnic Inst Department of Mathematical Sciences Dept of Mathematical Sciences [email protected] [email protected] 230 DS15 Abstracts

Peter R. Kramer to gain insights into how to predict structural differences Rensselaer Polytechnic Institute between healthy and cancerous tissue. Department of Mathematical Sciences [email protected] Jake P. Taylor-King Mathematical Institute, The University of Oxford. David Cai [email protected] Courant Institute for Mathematical Sciences, NYU Shanghai Jiao-Tong University Mason A. Porter [email protected] University of Oxford Oxford Centre for Industrial and Applied Mathematics [email protected] PP2 Wild Dynamics in Nonlinear Integrate-and-Fire Jon Chapman Neurons: Mixed-Mode Bursting, Spike Adding and Mathematical Institute Chaos. The University of Oxford [email protected] Nonlinear integrate-and-fire neuron models are hybrid dy- namical systems combining continuous differential equa- David Basanta tions and discrete resets, where spikes are defined by the Integrated Mathematical Oncology divergence of the membrane potential to infinity. The na- Moffitt Cancer Center ture of the spike pattern has been related to the orbits of [email protected] a discrete map, the adaptation map, which was studied in a number of situations where it was regular. We analyze here cases of discontinuous adaptation map and show that PP2 extremely wild behaviors can appear. On a FitzHugh-Nagumo Kinetic Model for Neural Networks Justyna H. Signerska INRIA MYCENAE Laboratory, Paris; This paper undertakes the analysis of the existence and Mathematical Neuroscience Lab, CIRB Coll`ege de France uniqueness of solutions for a mean-field FitzHugh-Nagumo [email protected] equation arising in the modeling of the macroscopic ac- tivity of the brain. In particular, we prove existence of Jonathan D. Touboul solution and non trivial stationary solution to evolution The Mathematical Neuroscience Laboratory equation without restriction on the connectivity coefficient College de France & INRIA Paris ε>0 and, using a semigroup factorisation method in Ba- [email protected] nach spaces, uniqueness of the stationary solution and its exponential NL stability in the small connectivity regime. Alexandre Vidal University of Evry-Val-d’Essonne Cristobal Quininao Department of Mathematics - Analysis and Probability Laboratoire Jacques-Louis Lions Lab [email protected] [email protected] Jonathan D. Touboul The Mathematical Neuroscience Laboratory PP2 College de France & INRIA Paris Return Times and Correlation Decay in Linked [email protected] Twist Maps St´ephane Mischler Linked twist maps form an archetypal class of non- Universit´e Paris-Dauphine uniformly hyperbolic system, of particular relevance to [email protected] fluid mixing. Previous results demonstrate that they have a polynomial decay of correlations. Of practical interest is the time at which the system begins to experience this alge- PP2 braic tail in the decay, after the faster, chaotic, exponential Examining Partial Cascades in Clustered Networks mixing has taken place. with High Intervertex Path Lengths

Rob Sturman There has been significant study of cascades on networks University of Leeds with various properties. There is a well-known branching [email protected] process approach developed by James Gleeson that is useful for sparse locally treelike networks, particularly those with low mean intervertex path lengths. We examine methods PP2 to apply to networks with longer intervertex path lengths, Osteocyte Network Formation which may contribute to a partial cascade not seen with Gleeson’s method. We construct a model of a dynamic network that consists of osteocytes, a type of cell within bone. On the bone-tissue Yosef M. Treitman interface, osteoblasts secrete the osteoid bone matrix and Rensselaer Polytechnic Institute multi-nucleated osteoclasts resorb it. These osteoblasts [email protected] can also differentiate into osteocytes. In pathological bone, the highly regulated bone remodelling signalling pathway Peter R. Kramer is disrupted. By understanding these dynamics, we hope Rensselaer Polytechnic Institute DS15 Abstracts 231

Department of Mathematical Sciences We applied our results to real traffic data from Minnesota [email protected] Transportation Department.

Chao Xia PP2 Brown University Almost Complete Separation of a Fluid Compo- chao [email protected] nent from a Mixture Using the Burgers Networks of Micro-separators Bjorn Sandstede, Paul Carter Division of Applied Mathematics Two ways of networking micro-separators to separate hy- Brown University drogen, for example, from a mixture almost completely bjorn [email protected], paul [email protected] are proposed. Each separator has two outlets for slightly higher and lower concentrations whose difference is mod- Laura Slivinski eled by a quadratic map of the average concentration at Woods Hole Oceanographic Institution its inlet. In the continuum the networks are governed by [email protected] the Burgers equation or its variant with nonlinear no-flux boundary conditions. The initial boundary value problem is exactly solvable. A family of equilibria attract globally. PP2 The target component is shown to be extracted from one side of a stationary shock. Micro-devices for testing the Stochastic Active-Transport Model of Cell Polar- idea are also proposed. ization

Shinya Watanabe We present a stochastic model of active vesicular trans- Mathematics & Informatics port and its role in cell po- larization, which takes into Ibaraki University account positive feedback between membrane-bound sig- [email protected] naling molecules and cytoskeletal filaments. In particular, we consider the cytoplasmic transport of vesicles on a two- dimensional cytoskeletal network, in which a vesicle con- Sohei Matsumoto taining signaling molecules can randomly switch between Research Center for Ubiquitous MEMS and Micro a diffusing state and a state of directed motion along a Engineering, filament. We show that the geometry of the cytoskeletal National Inst. of Advanced Industrial Science & filaments plays a crucial role in determining whether the Technology cell is capable of spontaneous cell polarization or only po- [email protected] larizes in response to an external chemical gradient.The former occurs if filaments are nucleated at sites on the cell Tomohiro Higurashi, Yuya Yoshikawa, Naoki Ono membrane (cortical actin), whereas the latter applies if the Department of Engineering Science and Mechanics filaments nucleate from organizing sites within the cyto- Shibaura Institute of Technology plasm (microtubule asters). [email protected], [email protected], [email protected] Bin Xu University of Utah, salt lake city,Utah [email protected] PP2 New Data Anysis Approach for Complex Signals Paul C. Bressloff with Low Signal to Noise Ratio’s University of Utah Department of Mathematics We propose a toolbox for signals comparisons with low bressloff@math.utah.edu SNR. We combine techniques from dynamical systems and information theory to quantify and extract information in the data sets. Data sets with SNR’s of 0.3 to 0.002 were an- PP2 alyzed. Useful information was found and quantized with tight bounds on the estimate. We also compare to Gaus- Statistical Properties of Finite Systems of Point- sian noise and show our toolbox can be used to separate Particles Interacting Through Binary Collisions signals with low SNR from white noise. In a finite system of point-particles interacting through bi- Jeremy Wojcik nary collisions, particles number of collisions and time of Georgia State University last collision are functions of the initial distributions of Dept. Mathematics and Statistics the positions and velocities of all particles. We investi- [email protected] gate a one-dimensional system of N particles interacting through either elastic or inelastic collisions. In particular, given random initial particle positions and velocities, we PP2 establish formulae for the distributions of the number of Data Assimilation for Traffic State and Parameter collisions and final collision times. Estimation Alexander L. Young Our goal is to apply data assimilation techniques to mi- University of Arizona croscopic and macroscopic traffic models to estimate traf- Program in Applied Mathematics fic states and parameters. We found ways in which sensor [email protected] data as well as GPS data of moving cars can be assimilated in a unified freeway. We implemented this approach using Joceline Lega both ensemble Kalman and particle filter and evaluated University of Arizona, USA their efficacy using microscopic and macroscopic models. [email protected] 232 DS15 Abstracts

Sunder Sethuraman University of Arizona Department of Mathematics [email protected]

PP2 Heteroclinic Separators of Magnetic Fields in Elec- trically Conducting Fluids

We partly solve the problem of existence of separators of a magnetic field in plasma. We single out in plasma a 3-body with a boundary in which the movement of plasma is of special kind which we call an (a-d)-motion. The statement of the problem and the suggested method for its solution lead to some theoretical problems from Dynamical Systems Theory. The work was supported by RFBR, Grants 12-01- 00672-a and 13-01-12452-ofi-m. Evgeny Zhuzhoma National Research University Higher School of Economics [email protected]

Vyatcheslav Grines, Timur Medvedev Lobachevsky State University of Nizhni Novgorod [email protected], [email protected]

Olga Pochinka National Research University Higher School of Economics [email protected] 2015 SIAM Conference on Applications of Dynamical Systems 233

Or­ganizer and Speaker Index

2015 234 2015 SIAM Conference on Applications of Dynamical Systems

B Berger, Mitchell, MS92, 1:30 Wed A Bergman, Lawrence, MS45, 9:00 Tue Abaid, Nicole, MS12, 10:00 Sun Bagrow, James, MS102, 1:30 Wed Bernoff, Andrew J., MS71, 4:00 Tue Abarbanel, Henry D., MS61, 1:30 Tue Bai, Lu, MS120, 9:00 Thu Bertozzi, Andrea L., IP2, 11:00 Mon Abarbanel, Henry D., MS101, 1:30 Wed Bakker, Berry, CP1, 5:50 Sun Bhattacharyya, Samit, CP8, 4:30 Sun Abel, Markus, MS53, 10:00 Tue Balasuriya, Sanjeeva, MS111, 8:30 Thu Bialonski, Stephan, PP2, 8:30 Wed Abramov, Rafail, MS69, 1:30 Tue Balasuriya, Sanjeeva, MS111, 10:00 Thu Bianco, Simone, MS67, 1:30 Tue Abramov, Rafail, MS69, 1:30 Tue Balasuriya, Sanjeeva, MS124, 1:30 Thu Bianco, Simone, MS67, 1:30 Tue Abrams, Daniel, MS12, 9:30 Sun Bamieh, Bassam A., MS124, 2:00 Thu Bick, Christian, MS27, 9:30 Mon Abud, Celso, PP1, 8:30 Tue Banerjee, Soumitro, MS49, 9:30 Tue Biktashev, Vadim N., MS80, 8:30 Wed Acosta-Humanez, Primitivo B., CP19, 4:45 Bansal, Shweta, MS85, 9:00 Wed Mon Barbaro, Alethea, MS11, 9:00 Sun Biktashev, Vadim N., MS80, 8:30 Wed Adams, Ronald, CP10, 5:30 Sun Barbaro, Alethea, MS11, 9:00 Sun Biktashev, Vadim N., MS93, 1:30 Wed Aguilar, Luis T., MS23, 9:30 Sun Barbaro, Alethea, MS29, 8:30 Mon Biktasheva, Irina, MS65, 1:30 Tue Aguirre, Pablo, MS57, 8:30 Tue Barkley, Dwight, MS80, 9:00 Wed Biktasheva, Irina, MS65, 1:30 Tue Aguirre, Pablo, MS108, 4:00 Wed Barranca, Victor, MS7, 9:00 Sun Biktasheva, Irina, MS73, 4:00 Tue Ahmad, Mohd Ashraf, MS54, 9:00 Tue Barranca, Victor, MS7, 9:00 Sun Billings, Lora, PD1, 7:00 Mon Ahn, Sungwoo, PP2, 8:30 Wed Barreiro, Andrea K., MS51, 8:30 Tue Birnir, Bjorn, MS11, 9:30 Sun Akao, Akihiko, PP1, 8:30 Tue Barreiro, Andrea K., MS51, 8:30 Tue Bittihn, Philip, MS64, 2:00 Tue Alacam, Deniz, PP2, 8:30 Wed Barreto, Ernest, MS117, 8:30 Thu Blackmore, Denis, MS39, 1:15 Mon Albers, David J., MS6, 1:30 Thu Barreto, Ernest, MS129, 1:30 Thu Blackmore, Denis, MS39, 1:15 Mon Albers, David J., MS6, 2:30 Thu Barrio, Roberto, MS119, 3:00 Wed Blackmore, Denis, MS52, 8:30 Tue Albers, John R., MS48, 8:30 Tue Barry, Anna M., MS100, 2:00 Wed Bloch, Anthony M., MS22, 8:30 Mon Alexeev, Timur, CP7, 4:30 Sun Bartoloni, Bruno, PP2, 8:30 Wed Blömker, Dirk, MS120, 8:30 Thu Al-Hdaibat, Bashir M., CP19, 3:45 Mon Barton, David A., CP6, 5:10 Sun Boatto, Stefanella, MS79, 8:30 Wed Alipova, Bakhyt, CP10, 4:30 Sun Basarab, Casayndra H., PP1, 8:30 Tue Boatto, Stefanella, MS79, 9:30 Wed Alolyan, Ibraheem, PP1, 8:30 Tue Basnarkov, Lasko, MS41, 2:45 Mon Boatto, Stefanella, MS92, 1:30 Wed Altaner, Bernhard, MS75, 4:00 Tue Basnayake, Ranil, PP2, 8:30 Wed Boccaletti, Stefano, MS68, 1:30 Tue Altaner, Bernhard, MS75, 4:00 Tue Bassett, Danielle, MS89, 9:30 Wed Bodenschatz, Eberhard, MS65, 2:00 Tue Amann, Andreas, CP11, 5:10 Sun Bates, Peter W., MS70, 2:30 Tue Boechler, Nicholas, MS83, 9:00 Wed Amann, Andreas, MS106, 4:00 Wed Bauver, Martha, PP1, 8:30 Tue Bogacz, Rafal, MS114, 9:30 Thu Ameli, Siavash, PP2, 8:30 Wed Beal, Aubrey N., MS43, 2:15 Mon Boie, Sebastian D., PP1, 8:30 Tue Ansmann, Gerrit, MS31, 9:00 Mon Beaume, Cedric, CP14, 3:45 Mon Bollt, Erik, MS44, 1:45 Mon Aoi, Shinya, MS112, 8:30 Thu Bellman, Jacob, PP2, 8:30 Wed Bondarenko, Vladimir E., CP21, 4:25 Mon Aoki, Takaaki, CP3, 5:10 Sun Bellsky, Thomas, MS63, 2:00 Tue Bonet, Carles, CP9, 4:50 Sun Arbabi, Hassan, MS42, 1:45 Mon Belykh, Igor, MS12, 9:00 Sun Bose, Amitabha, MS25, 8:30 Mon Argyris, Apostolos, PP2, 8:30 Wed Belykh, Igor, MS12, 9:00 Sun Bose, Amitabha, MS25, 8:30 Mon Arioli, Gianni, CP7, 5:50 Sun Belykh, Igor, MS30, 8:30 Mon Bose, Chris, MS44, 1:15 Mon Arloff, William D., PP1, 8:30 Tue Benichou, Olivier, MS81, 10:00 Wed Bose, Chris, MS44, 1:15 Mon Arroyo-Almanza, Diana A., CP23, 5:25 Mon Ben-Naim, Eli, PD1, 7:00 Mon Bossolini, Elena, PP2, 8:30 Wed Assaf, Michael, MS46, 8:30 Tue Berdeni, Yani, MS133, 2:30 Thu Bounkhel, Messaoud, MS91, 3:00 Wed Assaf, Michael, MS46, 8:30 Tue Berg, Sebastian, MS15, 3:00 Sun Braatz, Richard D., MS82, 8:30 Wed Avedisov, Sergei S., CP3, 4:30 Sun

Italicized names indicate session organizers. 2015 SIAM Conference on Applications of Dynamical Systems 235

Bradley, Elizabeth, CP22, 4:25 Mon Chan, Matthew H., PP1, 8:30 Tue D Brena-Medina, Victor F., CP29, 4:40 Tue Chandrashekar, Pooja, PP2, 8:30 Wed Dalena, Serena, PD1, 7:00 Mon Bressloff, Paul C., MS105, 4:00 Wed Charalampidis, Efstathios, CP23, 4:05 Mon Dankowicz, Harry, MS100, 3:00 Wed Bröcker, Jochen, MS61, 1:30 Tue Chen, Diandian Diana, MS28, 8:30 Mon Das, Sanjukta, CP11, 5:30 Sun Bröcker, Jochen, MS61, 1:30 Tue Chen, Qianting, PP1, 8:30 Tue Dawes, Jonathan, PP2, 8:30 Wed Brons, Morten, MS52, 10:00 Tue Chen, Xiaopeng, MS120, 8:30 Thu Dawson, Scott, MS55, 9:00 Tue Brooks, Heather A., PP2, 8:30 Wed Chen, Xiaopeng, MS132, 1:30 Thu Day, Sarah, MS128, 2:30 Thu Brubaker, Douglas, MS29, 8:30 Mon Chen, Xiaopeng, MS132, 2:30 Thu de Barros Viglioni, Humberto H., MS79, Brunel, Nicolas, MS74, 4:30 Tue Cherry, Elizabeth M., MS15, 2:00 Sun 10:00 Wed Brunton, Bing W., MS42, 2:45 Mon Cherry, Elizabeth M., MS65, 2:30 Tue De Maesschalck, Peter, MS118, 9:00 Thu Brunton, Steven, MS42, 1:15 Mon Cheviakov, Alexei F., MS81, 9:00 Wed De Rijk, Björn, MS70, 3:00 Tue Brunton, Steven, MS55, 8:30 Tue Chong, Antonio S., PP1, 8:30 Tue De Sousa, Meirielen C., PP1, 8:30 Tue Brunton, Steven, MS55, 10:00 Tue Chong, Christopher, MS45, 9:30 Tue del Genio, Charo I., MS68, 1:30 Tue Budanur, Nazmi Burak, CP19, 4:25 Mon Christov, Ivan C., MS39, 2:45 Mon del Genio, Charo I., MS68, 2:30 Tue Budd, Chris, MS36, 1:15 Mon Chuang, Yaoli, MS88, 9:30 Wed Della Rossa, Fabio, CP18, 4:25 Mon Budisic, Marko, MS92, 3:00 Wed Ciocanel, Veronica M., PP2, 8:30 Wed Dellnitz, Michael, MS103, 2:30 Wed Budisic, Marko, MS111, 8:30 Thu Clifton, Sara, CP5, 4:30 Sun Denner, Andreas, MS103, 3:00 Wed Budisic, Marko, MS124, 1:30 Thu Cogan, Nick, MS90, 8:30 Wed DeSantis, Mark, CP26, 4:00 Tue Burke, Korana, CP15, 5:25 Mon Cohen, Seth D., MS43, 1:45 Mon Desbrun, Mathieu, MS79, 8:30 Wed Burke, Korana, MS62, 1:30 Tue Collens, Jarod, MS50, 9:00 Tue Desroches, Mathieu, MS118, 8:30 Thu Burli, Pralhad, PP1, 8:30 Tue Colombo, Giovanni, MS78, 9:30 Wed Desroches, Mathieu, MS130, 1:30 Thu Butlin, Tore, MS133, 3:00 Thu Colonius, Fritz, CP19, 4:05 Mon Desroches, Mathieu, MS130, 2:30 Thu Byrne, Greg A., MS28, 9:00 Mon Comtois, Philippe, MS65, 3:00 Tue D’Huys, Otti, MS2, 10:30 Sun Consagra, William, PP2, 8:30 Wed Dias, Juliana, MS48, 8:30 Tue C Contreras, Christy, PP1, 8:30 Tue Dias, Juliana, MS48, 9:30 Tue Cafaro, Carlo, CP18, 5:25 Mon Conway, Jessica M., MS85, 8:30 Wed Dierckx, Hans, MS80, 9:30 Wed Caiola, Michael, PP1, 8:30 Tue Conway, Jessica M., MS98, 1:30 Wed Ding, Xiong, CP10, 5:50 Sun Caldas, Iberê L., MS24, 10:00 Mon Conway, Jessica M., MS98, 2:00 Wed Dobreva, Atanaska, MS90, 9:30 Wed Calderer, Maria-Carme, MS97, 4:00 Tue Corron, Ned J., MS43, 1:15 Mon Doelman, Arjen, MS19, 10:00 Mon Camp, Charles D., CP12, 5:30 Sun Corron, Ned J., MS43, 1:15 Mon Doelman, Arjen, MS123, 1:30 Thu Campbell, David, PD1, 7:00 Mon Cousins, Will, MS110, 9:30 Thu Doering, Charles, PD1, 7:00 Mon Campbell, Sue Ann, CP22, 3:45 Mon Creaser, Jennifer L., MS57, 9:30 Tue Donohue, John G., CP5, 5:30 Sun Canadell, Marta, PP2, 8:30 Wed Criado, Regino, MS68, 1:30 Tue Dorfler, Florian, MS107, 4:00 Wed Candelier, Fabien, MS35, 2:15 Mon Criado, Regino, MS68, 1:30 Tue Dorfler, Florian, MS107, 4:30 Wed Carja, Oana, MS67, 3:00 Tue Cumings, Karen M., PP2, 8:30 Wed D’Orsogna, Maria, MS81, 8:30 Wed Carr, Thomas W., PP2, 8:30 Wed Cummings, Linda, MS124, 3:00 Thu Dostal, Leo, CP10, 5:10 Sun Carroll, Samuel R., MS66, 3:00 Tue Cummins, Bree, PP1, 8:30 Tue Drotos, Gabor, MS58, 3:00 Tue Carroll, Thomas L., MS101, 1:30 Wed Curran, Mark J., CP1, 4:50 Sun Duan, Jinqiao, MS120, 8:30 Thu Carroll, Thomas L., MS101, 3:00 Wed Czechowski, Aleksander, CP1, 5:30 Sun Duan, Jinqiao, MS132, 1:30 Thu Carter, Paul A., MS40, 1:15 Mon Duan, Jinqiao, MS132, 1:30 Thu Carter, Paul A., MS70, 2:00 Tue Duncan, Jacob P., CP5, 4:50 Sun Champneys, Alan R., MS112, 8:30 Thu

Italicized names indicate session organizers. 236 2015 SIAM Conference on Applications of Dynamical Systems

Dunworth, Jeff, PP2, 8:30 Wed Folias, Stefanos, MS74, 4:00 Tue Giusti, Chad, MS14, 2:00 Sun Durazo, Juan, MS63, 2:30 Tue Follmann, Rosangela, MS59, 1:30 Tue Glasner, Karl, MS1, 9:30 Sun Düren, Philipp, PP1, 8:30 Tue Forgoston, Eric, MS3, 9:00 Sun Glass, Leon, MS2, 10:00 Sun Duriez, Thomas, MS111, 9:30 Thu Forgoston, Eric, MS21, 8:30 Mon Glendinning, Paul, MS87, 9:00 Wed Dyachenko, Sergey, CP24, 4:05 Mon Forgoston, Eric, MT2, 4:00 Wed Gluckman, Bruce J., MS6, 3:00 Thu Dzakpasu, Rhonda, MS84, 10:00 Wed Forgoston, Eric, MT2, 4:00 Wed Godec, Aljaz, MS81, 9:30 Wed Fox, Adam M., MS24, 9:30 Mon Goel, Pranay, MS109, 5:30 Wed E Gog, Julia R., MS85, 10:00 Wed Ebadi, Sepideh, PP2, 8:30 Wed Fraden, Seth, MS76, 4:30 Tue Goh, Ryan, PP1, 8:30 Tue Ecke, Robert E., CP14, 4:25 Mon Franci, Alessio, MS130, 2:00 Thu Golubitsky, Martin, MS20, 10:00 Mon Edelman, Mark, CP11, 4:50 Sun Francoise, Jean-Pierre, MS118, 8:30 Thu Gomez, Marcella, MS17, 3:30 Sun Eden, Uri, MS114, 10:00 Thu Freestone, Dean R., CP18, 5:05 Mon Gong, Xue, PP2, 8:30 Wed Edwards, Roderick, MS2, 9:00 Sun Frey, Hans-Peter, MS6, 2:00 Thu Gonzalez, Marta, MS16, 2:30 Sun Edwards, Roderick, MS2, 9:30 Sun Froyland, Gary, MS103, 1:30 Wed Gonzalez Tokman, Cecilia, MS44, 2:15 Mon Eisenberg, Marisa, CP8, 5:50 Sun Froyland, Gary, MS103, 1:30 Wed Gore, Jeff, IP5, 11:00 Wed Ekrut, David A., CP2, 4:30 Sun Fuller, Pamela B., MS51, 8:30 Tue Gorur-Shandilya, Srinivas, MS115, 9:30 Thu Emenheiser, Jeff, MS62, 2:00 Tue Fuller, Pamela B., MS51, 9:00 Tue Gowda, Karna V., PP1, 8:30 Tue Enden, Giora, MS97, 4:30 Tue Funato, Tetsuro, MS112, 9:30 Thu Gowen, Savannah, MS86, 9:30 Wed Erickson, Brittany, MS11, 9:00 Sun G Granados, Albert, MS116, 10:00 Sun Erickson, Brittany, MS11, 10:30 Sun Gajamannage, Kelum D., CP19, 5:05 Mon Green, Kevin R., PP2, 8:30 Wed Erickson, Brittany, MS29, 8:30 Mon Galanthay, Theodore E., CP11, 5:50 Sun Grigoriev, Roman, MS80, 8:30 Wed Ermentrout, Bard, IP4, 11:00 Tue Galuzio, Paulo, CP23, 3:45 Mon Grigoriev, Roman, MS93, 1:30 Wed Ermentrout, Bard, MS66, 1:30 Tue Gandhi, Punit R., CP13, 4:30 Sun Grinberg, Itay, MS96, 2:00 Wed Ermentrout, Bard, MS74, 4:00 Tue Garg, Piyush, PP2, 8:30 Wed Grooms, Ian, MS8, 9:00 Sun Garland, Joshua, CP4, 5:10 Sun Eubank, Stephen, MS89, 9:00 Wed Groothedde, Chris M., PP1, 8:30 Tue Gauthier, Daniel J., MS31, 10:00 Mon Grover, Piyush, CP4, 6:10 Sun F Gedeon, Tomas, MS2, 9:00 Sun Fahroo, Fariba, PD2, 12:00 Tue Grudzien, Colin J., CP10, 4:50 Sun Gedeon, Tomas, MS2, 9:00 Sun Fairchild, Michael, MS4, 10:00 Sun Gu, Shi, PP2, 8:30 Wed Gelfreich, Vassili, MS119, 1:30 Wed Farazmand, Mohammad, CP19, 5:25 Mon Guckenheimer, John, SP1, 8:15 Sun Gendelman, Oleg, MS32, 1:15 Mon Farjami, Saeed, PP1, 8:30 Tue Gudoshnikov, Ivan, MS91, 2:30 Wed Gendelman, Oleg, MS32, 1:15 Mon Fatkullin, Ibrahim, CP24, 5:05 Mon Guo, Yixin, MS84, 9:30 Wed Gendelman, Oleg, MS45, 8:30 Tue Fatkullin, Ibrahim, MS69, 1:30 Tue Guo, Yixin, MS114, 8:30 Thu Geng, Jiansheng, CP23, 4:25 Mon Fenton, Flavio, MS126, 1:30 Thu Gurevich, Pavel, MS23, 10:00 Sun Georgescu, Michael, MS41, 1:45 Mon Fernandez, Oscar, MS4, 10:30 Sun Guseva, Ksenia, MS35, 2:45 Mon Ghazaryan, Anna, MS122, 8:30 Thu Fernandez-Garcia, Soledad, MS118, 9:30 Thu Ghazaryan, Anna, MS134, 1:30 Thu H Haas, Jesse, PP1, 8:30 Tue Fessel, Kimberly, CP8, 6:10 Sun Ghazaryan, Anna, MS134, 3:00 Thu Hackbarth, Axel, MS21, 9:30 Mon Feudel, Ulrike, MS31, 8:30 Mon Ghil, Michael, MS58, 1:30 Tue Hafkenscheid, Patrick, MS56, 10:00 Tue Feudel, Ulrike, MS31, 8:30 Mon Ghil, Michael, MS58, 1:30 Tue Hagerstrom, Aaron M., CP22, 4:45 Mon Filo, Maurice G., CP8, 4:50 Sun Ghosh, Suma, CP5, 5:10 Sun Hale, Sidni, PP2, 8:30 Wed Fitzpatrick, Ben G., CP3, 5:30 Sun Ghrist, Robert W., MS14, 2:00 Sun Haley, James M., CP26, 4:20 Tue Flaßkamp, Kathrin, CP11, 6:10 Sun Girvan, Michelle, MT1, 2:00 Sun Hallatschek, Oskar, MS67, 2:30 Tue Giusti, Chad, MS14, 2:00 Sun Hamilton, Franz, MS15, 2:30 Sun Italicized names indicate session organizers. 2015 SIAM Conference on Applications of Dynamical Systems 237

Hamzi, Boumediene, CP15, 3:45 Mon Hripcsak, George, MS6, 1:30 Thu K Han, Jung Min, PP1, 8:30 Tue Hsieh, Ani, MS3, 9:00 Sun Kang, Wei, MS37, 1:15 Mon Handy, Gregory A., PP2, 8:30 Wed Hsieh, Ani, MS3, 9:00 Sun Kao, Hsien-Ching, CP13, 4:50 Sun Haragus, Mariana, MS122, 8:30 Thu Hsieh, Ani, MS21, 8:30 Mon Kapitaniak, Tomasz, CP13, 5:10 Sun Harker, Shaun, MS56, 9:00 Tue Hu, David, MS71, 4:30 Tue Kapitanov, Georgi, MS34, 1:45 Mon Harley, Kristen, MS77, 5:00 Tue Huddy, Stanley R., PP2, 8:30 Wed Kapitula, Todd, MS19, 9:30 Mon Harris, Jeremy D., MS87, 9:30 Wed Humpherys, Jeffrey, MS134, 1:30 Thu Karamchandani, Avinash J., CP13, 5:50 Sun Harris, Kameron D., MS5, 9:30 Mon Hungria, Allan R., PP2, 8:30 Wed Karamched, Bhargav R., PP1, 8:30 Tue Hartmann, Carsten, MS82, 9:00 Wed Hupkes, Hermen Jan, MS70, 1:30 Tue Karim, Md. Shahriar, CP2, 5:30 Sun Hasan, Ragheb, PP1, 8:30 Tue Hupkes, Hermen Jan, MS70, 1:30 Tue Karrasch, Daniel, MS104, 5:30 Wed Hauert, Christoph, MS88, 10:00 Wed Hupkes, Hermen Jan, MS77, 4:00 Tue Kasti, Dinesh, CP4, 4:50 Sun Hauser, Marcus, MS73, 4:00 Tue Kath, William, MS33, 2:45 Mon Hawkins, Russell, MS62, 1:30 Tue I Keane, Andrew, MS106, 5:30 Wed Iams, Sarah, MS123, 3:00 Thu Hayashi, Michael A., PP2, 8:30 Wed Kelley, Aaron, PP2, 8:30 Wed Ide, Kayo, MS37, 1:45 Mon He, YanYan, MS90, 10:00 Wed Kelley, Douglas H., MS99, 2:00 Wed Illing, Lucas, MS43, 1:15 Mon Heckman, Christoffer R., MS3, 10:30 Sun Kelly, Scott D., MS4, 9:00 Sun Illing, Lucas, MS43, 2:45 Mon Heckman, Christoffer R., MS33, 1:15 Kelly, Scott D., MS52, 8:30 Tue Mon Imura, Jun-ichi, MS41, 1:15 Mon Kempton, Louis, MS30, 9:30 Mon Heffernan, Jane, MS85, 8:30 Wed Imura, Jun-ichi, MS41, 2:15 Mon Kenett, Dror Y., MS89, 10:00 Wed Hernandez-Duenas, Gerardo, MS8, 10:00 Imura, Jun-ichi, MS54, 8:30 Tue Kepley, Shane D., CP10, 6:10 Sun Sun Ippei, Obayashi, MS112, 9:00 Thu Kevrekidis, I. G., MS110, 10:00 Thu Herschlag, Gregory J., MS13, 10:30 Sun Iron, David, MS38, 1:45 Mon Kevrekidis, Panayotis, MS1, 10:00 Sun Hess, Kathryn, MS14, 2:30 Sun Khan, Muhammad D., CP29, 4:00 Tue Higuera, Maria, CP14, 4:05 Mon J Khanin, Kostantin, MS92, 2:00 Wed Hill, Kaitlin, MS36, 2:15 Mon Jacobs, Henry O., MS131, 1:30 Thu Khasin, Michael, MT2, 4:00 Wed Hines, Paul, MS107, 5:00 Wed Jacobs, Henry O., MS131, 2:30 Thu Kieu, Thinh T., CP4, 4:30 Sun Hirata, Yoshito, MS41, 1:15 Mon Jacobsen, Karly, CP3, 5:50 Sun Kile, Jennifer, MS51, 9:30 Tue Hirata, Yoshito, MS41, 1:15 Mon James, Guillaume, MS83, 9:30 Wed Kiliç, Deniz K., PP1, 8:30 Tue Hirata, Yoshito, MS54, 8:30 Tue James, Ryan G., MS75, 5:00 Tue Kilpatrick, Zachary, MS27, 9:00 Mon Hittmeyer, Stefanie, MS108, 4:00 Wed Jaramillo, Gabriela, PP1, 8:30 Tue Jarrett, Angela M., MS90, 8:30 Wed Kilpatrick, Zachary, MS66, 1:30 Tue Hittmeyer, Stefanie, MS108, 4:00 Wed Jeffrey, Mike R., MS100, 1:30 Wed Kilpatrick, Zachary, MS74, 4:00 Tue Hjorth, Poul G., CP18, 4:05 Mon Jeter, Russell, PP2, 8:30 Wed Hoffman, Matthew J., MS15, 2:00 Sun Kim, Peter S., MS34, 1:15 Mon Ji, Yanyan, MS126, 2:30 Thu Hogan, John, CP9, 5:30 Sun Kirk, Vivien, MS118, 8:30 Thu Jiang, Jifa, MS120, 10:00 Thu Holmes, Philip, MS112, 8:30 Thu Kirk, Vivien, MS130, 1:30 Thu Jiang, Yazhen, CP4, 5:50 Sun Holzer, Matt, MS134, 2:00 Thu Kirk, Vivien, MS130, 1:30 Thu Jones, Barbara, MS67, 2:00 Tue Homer, Martin, CP9, 5:10 Sun Kirst, Christoph, MS127, 2:00 Thu Jones, Kimberley, MS99, 1:30 Wed Horan, Joseph, MS44, 2:45 Mon Kiss, Istvan Z., MS76, 4:00 Tue Joshi, Badal, MS25, 9:30 Mon Horesh, Raya, CP28, 4:40 Tue Knapper, Drake, PP1, 8:30 Tue Just, Winfried, CP8, 5:10 Sun Hoshino, Hikaru, PP1, 8:30 Tue Knobloch, Edgar, PD1, 7:00 Mon Hoyer-Leitzel, Alanna, MS36, 2:45 Mon Kogan, Oleg B., CP29, 5:00 Tue

Italicized names indicate session organizers. 238 2015 SIAM Conference on Applications of Dynamical Systems

Köksal Ersöz, Elif, PP2, 8:30 Wed Lecoanet, Daniel, MS8, 9:00 Sun Ma, Yiping, MS113, 9:00 Thu Kolokolnikov, Theodore, MS40, 1:45 Mon Lee, Rachel, MS71, 5:00 Tue Macau, Elbert E., MS59, 1:30 Tue Kolokolnikov, Theodore, MS105, 4:00 Lee, Seungjoon, MS110, 9:00 Thu Macau, Elbert E., MS59, 2:30 Tue Wed Lega, Joceline, PD1, 7:00 Mon Macau, Elbert E., MS72, 4:00 Tue Koltai, Peter, MS103, 2:00 Wed Lehnert, Judith, MS106, 5:00 Wed Macdonald, John, MS112, 10:00 Thu Komarov, Maxim, MS117, 9:30 Thu Lehnertz, Klaus, MS31, 8:30 Mon Madruga, Santiago, CP6, 4:30 Sun Komatsuzaki, Tamiki, MS95, 2:00 Wed Lehnertz, Klaus, MS115, 8:30 Thu Mahoney, John R., MS86, 8:30 Wed Koon, Wang-Sang, MS95, 1:30 Wed Leifeld, Julie, MS49, 9:00 Tue Mahoney, John R., MS86, 8:30 Wed Korda, Milan, MS131, 1:30 Thu Leisman, Katelyn J., PP2, 8:30 Wed Mahoney, John R., MS99, 1:30 Wed Korniss, Gyorgy, MS16, 2:00 Sun Leite da Silva Dias, Pedro, MS48, 10:00 Tue Makarenkov, Oleg, MS78, 8:30 Wed Korniss, Gyorgy, MS16, 2:00 Sun Leok, Melvin, MS22, 9:30 Mon Makarenkov, Oleg, MS78, 8:30 Wed Korotkevich, Alexander O., CP24, 4:25 Mon Lermusiaux, Pierre, MS21, 10:00 Mon Makarenkov, Oleg, MS91, 1:30 Wed Kosiuk, Ilona, CP5, 5:50 Sun Lessard, Jean-Philippe, MS56, 8:30 Tue Makrides, Elizabeth J., MS19, 9:00 Mon Kovacic, Gregor, MS69, 2:00 Tue Levanova, Tatiana A., PP1, 8:30 Tue Malik, Nishant, MS89, 8:30 Wed Kraitzman, Noa, MS1, 9:00 Sun Levien, Ethan, PP2, 8:30 Wed Malik, Nishant, MS89, 8:30 Wed Kraitzman, Noa, MS1, 9:00 Sun Levnajic, Zoran, MS127, 2:30 Thu Malik, Nishant, MS102, 1:30 Wed Kraitzman, Noa, MS19, 8:30 Mon Lewis, Tim, MS25, 10:00 Mon Mallela, Abhishek, CP28, 4:20 Tue Kramer, Peter R., MS29, 9:00 Mon Li, Songting, MS7, 9:30 Sun Malomed, Boris, MS96, 3:00 Wed Kramer, Sean, CP4, 5:30 Sun Li, Yao, CP29, 4:20 Tue Mandal, Dibyendu, MS75, 4:30 Tue Krauskopf, Bernd, MS119, 2:30 Wed Lilienkamp, Thomas, CP1, 5:10 Sun Manevich, Leonid, MS96, 1:30 Wed Kristiansen, Kristian Uldall, CP9, 4:30 Sun Lin, Kevin K., CP15, 4:25 Mon Mangan, Niall M., MS38, 1:15 Mon Krumscheid, Sebastian, MS95, 3:00 Wed Lin, Lucas, PP1, 8:30 Tue Mangan, Niall M., MS38, 1:15 Mon Kuehn, Christian, MS13, 9:30 Sun Lindenberg, Katja, MS105, 4:30 Wed Manukian, Vahagn, MS122, 8:30 Thu Kulp, Christopher W., PP1, 8:30 Tue Lindsay, Alan E., MS81, 8:30 Wed Manukian, Vahagn, MS122, 10:00 Thu Kurebayashi, Wataru, CP17, 4:25 Mon Lindsay, Alan E., MS94, 1:30 Wed Manukian, Vahagn, MS134, 1:30 Thu Kuroda, Shigeru, PP2, 8:30 Wed Lindsay, Alan E., MS94, 2:00 Wed Marcotte, Christopher, MS80, 10:00 Wed Kurths, Juergen, MS41, 1:15 Mon Lipson, Hod, IP7, 4:15 Thu Martens, Erik A., MS117, 9:00 Thu Kurths, Juergen, MS54, 8:30 Tue Liu, Di, MS69, 2:30 Tue Martins, Caroline G. L., MS24, 9:00 Mon Kurths, Juergen, MS54, 8:30 Tue Lizarraga, Ian M., MS108, 5:00 Wed Masoller, Cristina, MS33, 2:15 Mon Kuske, Rachel, MS17, 2:30 Sun Lloyd, Alun, MS85, 9:30 Wed Mason, Gemma, MS4, 9:30 Sun Kutz, J. Nathan, MS60, 2:30 Tue Locke, Rory A., PP2, 8:30 Wed Matheny, Matt, MS62, 2:30 Tue Loire, Sophie, MS111, 9:00 Thu Mauro, Ava, MS94, 2:30 Wed L Lolla, Tapovan, MS37, 2:45 Mon Lafortune, Stéphane, MS134, 2:30 Thu Mauroy, Alexandre, MS47, 10:00 Tue Lombardi, Éric, MS119, 2:00 Wed Lagor, Frank D., MS37, 2:15 Mon Mazzoleni, Michael J., CP21, 3:45 Mon Lopes, Sergio R., MS72, 5:00 Tue Laing, Carlo R., MS129, 1:30 Thu Mcavity, David, CP21, 4:05 Mon Lopez, Vanessa, CP23, 4:45 Mon Lajoie, Guillaume, MS75, 4:00 Tue Mccalla, Scott, MS88, 8:30 Wed Lundell, Fredrik, MS35, 1:45 Mon Lajoie, Guillaume, MS75, 5:30 Tue Mccalla, Scott, MS88, 8:30 Wed Lushnikov, Pavel M., CP24, 4:45 Mon Larremore, Daniel B., MS5, 9:00 Mon McClure, James E., PP2, 8:30 Wed Layton, Jessica, CP12, 5:10 Sun M McCullen, Nick, PP1, 8:30 Tue Lazaro, J. Tomas, MS119, 1:30 Wed Ma, Baoling, CP21, 5:05 Mon Mcdougall, Damon, MS21, 8:30 Mon Leach, Andrew, PP1, 8:30 Tue Ma, Tian, PP1, 8:30 Tue Mcgee, Reginald, PP2, 8:30 Wed

Italicized names indicate session organizers. 2015 SIAM Conference on Applications of Dynamical Systems 239

McKinley, Scott, MS13, 10:00 Sun N Ouellette, Nicholas T., MS124, 2:30 Thu Mcquighan, Kelly, MS70, 1:30 Tue Nagel, Rainer, MS47, 9:00 Tue Ovsyannikov, Ivan, MS57, 8:30 Tue Mcquighan, Kelly, MS77, 4:00 Tue Naik, Shibabrat, CP6, 5:30 Sun Ovsyannikov, Ivan, MS57, 9:00 Tue Mcquighan, Kelly, MS122, 9:30 Thu Nakagaki, Toshiyuki, PP2, 8:30 Wed Medeiros, Everton S., PP1, 8:30 Tue P Nakao, Hiroya, CP3, 4:50 Sun Padberg-Gehle, Kathrin, MS103, 1:30 Meerman, Corine J., PP2, 8:30 Wed Nanda, Vidit, MS56, 9:30 Tue Wed Mehlig, Bernhard, MS35, 1:15 Mon Nayak, Alok R., MS64, 2:30 Tue Padberg-Gehle, Kathrin, MS124, 1:30 Thu Mehlig, Bernhard, MS35, 1:15 Mon Neamtu, Alexandra, MS132, 2:00 Thu Paley, Derek A., MS37, 1:15 Mon Meiss, James D., CP17, 4:45 Mon Neda, Zoltan, MS16, 3:00 Sun Palmer, Cody, PP1, 8:30 Tue Mendoza, Joshua, PP1, 8:30 Tue Neofytou, Giannis, PP1, 8:30 Tue Panfilov, Alexander, MS73, 4:30 Tue Merrison-Hort, Robert, MS114, 9:00 Thu Nepomnyashchy, Alexander, MS97, 4:00 Park, Paul, CP17, 5:25 Mon Tue Metcalfe, Guy, MS26, 9:00 Mon Park, Youngmin, PP1, 8:30 Tue Nepomnyashchy, Alexander, MS97, 5:30 Tue Meyer, Evgeny, MS10, 10:00 Sun Parlitz, Ulrich, CP2, 6:10 Sun Neskovic, Predrag, PD2, 12:00 Tue Mezic, Igor, MS47, 8:30 Tue Parlitz, Ulrich, MS61, 1:30 Tue Neville, Rachel, MS9, 10:30 Sun Mezic, Igor, MS47, 8:30 Tue Pasqualetti, Fabio, MS89, 9:30 Wed Newby, Jay, MS94, 1:30 Wed Mezic, Igor, PD2, 12:00 Tue Patel, Mainak, MS51, 10:00 Tue Newhall, Katherine, MS13, 9:00 Sun Mezic, Igor, MS60, 1:30 Tue Paul, Mark, MS99, 3:00 Wed Newhall, Katherine, MS13, 9:00 Sun Mier-y-Teran, Luis, CP8, 5:30 Sun Pazó, Diego, MS129, 2:00 Thu Nguyen, Hoang, MS91, 2:00 Wed Mier-y-Teran, Luis, MS71, 4:00 Tue Peckham, Bruce B., CP17, 5:05 Mon Nicola, Wilten, PP2, 8:30 Wed Mireles James, Jason, MS108, 4:30 Wed Pecora, Louis M., MT1, 2:00 Sun Nieddu, Garrett, PP1, 8:30 Tue Mireles-James, Jason, MS128, 1:30 Thu Pecora, Louis M., MS20, 9:00 Mon Nijholt, Eddie, MS27, 8:30 Mon Mitchell, Kevin A., MS86, 8:30 Wed Pelinovsky, Dmitry, MS83, 10:00 Wed Nijholt, Eddie, MS27, 8:30 Mon Mitchell, Kevin A., MS99, 1:30 Wed Pereira, Tiago, MS27, 10:00 Mon Nishikawa, Takashi, MS20, 8:30 Mon Mitchell, Kevin A., MS99, 2:30 Wed Petrovskii, Sergei, MS123, 1:30 Thu Nishikawa, Takashi, MS20, 8:30 Mon Moehlis, Jeff, IP6, 11:15 Thu Picardo, Jason R., CP1, 6:10 Sun Nitzan, Mor, MS115, 10:00 Thu Moehlis, Jeff, MS109, 4:00 Wed Pikovsky, Arkady, MS117, 8:30 Thu Noel, Pierre-Andre, MS5, 10:00 Mon Mohapatra, Anushaya, CP21, 4:45 Mon Pikovsky, Arkady, MS117, 8:30 Thu Norton, Kerri-Ann, MS38, 2:45 Mon Mohr, Ryan, MS47, 9:30 Tue Pikovsky, Arkady, MS129, 1:30 Thu Nykamp, Duane, MS66, 2:30 Tue Molkov, Yaroslav, PP2, 8:30 Wed Pillai, Dipin S., CP25, 4:05 Mon Moore, Richard O., MT2, 4:00 Wed O Piltz, Sofia, MS87, 10:00 Wed Morales Morales, Jose Eduardo, CP2, 5:50 Ober-Bloebaum, Sina, MS82, 9:30 Wed Pina, Jason E., PP2, 8:30 Wed Sun Olaniyi, Samson, PP2, 8:30 Wed Pisarchik, Alexander N., MS31, 9:30 Mon Morone, Uriel I., MS61, 2:30 Tue Olivar Tost, Gerard, CP26, 4:40 Tue Plum, Michael, MS128, 3:00 Thu Morrison, P. J., MS24, 8:30 Mon Olmos, Daniel, MS93, 3:00 Wed Poignard, Camille, CP2, 4:50 Sun Motta, Francis C., MS9, 10:00 Sun Onozaki, Kaori, CP17, 4:05 Mon Politi, Antonio, MS72, 4:00 Tue Motter, Adilson E., IP1, 11:45 Sun Orosz, Gabor, MS17, 2:00 Sun Poll, Daniel, PP1, 8:30 Tue Mugler, Andrew, MS46, 9:00 Tue Orosz, Gabor, MS17, 2:00 Sun Poon, Philip, CP6, 6:10 Sun Munsky, Brian, MS46, 9:30 Tue Oshanin, Gleb, MS105, 5:00 Wed Porfiri, Maurizio, MS12, 9:00 Sun Murthy, Abhishek, CP11, 4:30 Sun Osinga, Hinke M., MS104, 5:00 Wed Porfiri, Maurizio, MS30, 8:30 Mon Muthusamy, Lakshmanan, CP13, 5:30 Sun Otani, Niels, MS93, 1:30 Wed Porfiri, Maurizio, MS30, 8:30 Mon Mutua, Jones M., PP1, 8:30 Tue Ott, Edward, MS58, 2:30 Tue Porter, Jeff, CP24, 3:45 Mon

Italicized names indicate session organizers. 240 2015 SIAM Conference on Applications of Dynamical Systems

Porter, Mason A., MT1, 2:00 Sun Roberts, Andrew, MS49, 8:30 Tue S Pozo, Roldan, MS102, 2:00 Wed Roberts, Andrew, MS49, 8:30 Tue Sacré, Pierre, CP27, 5:40 Tue Pratt, Larry, MS26, 9:30 Mon Roberts, Anthony J., MS110, 8:30 Thu Sadeghpour, Mehdi, CP22, 4:05 Mon Proctor, Joshua L., MS42, 2:15 Mon Roberts, Anthony J., MS110, 8:30 Thu Salih, Rizgar, CP17, 3:45 Mon Promislow, Keith, MS1, 9:00 Sun Roberts, Kerry-Lyn, MS116, 9:00 Sun Sander, Evelyn, MS57, 10:00 Tue Promislow, Keith, MS19, 8:30 Mon Roberts, Kerry-Lyn, MS116, 9:30 Sun Sanders, David P., CP15, 4:45 Mon Prykarpatski, Anatolij, MS39, 1:45 Mon Roberts, Lewis G., MS107, 4:00 Wed Sandstede, Bjorn, MS1, 10:30 Sun Putelat, Thibaut, MS121, 8:30 Thu Roberts, Lewis G., MS107, 4:00 Wed Sandstede, Bjorn, PD1, 7:00 Mon Putkaradze, Vakhtang, MS22, 8:30 Mon Rodriguez, Jairo, MS93, 2:30 Wed Sanz-Alonso, Daniel, MS61, 2:00 Tue Putkaradze, Vakhtang, MS22, 9:00 Mon Rodriguez, Marcos, MS50, 8:30 Tue Sapsis, Themistoklis, MS32, 1:45 Mon Rodriguez, Marcos, MS50, 8:30 Tue Sarma, Sridevi, MS109, 5:00 Wed Q Rodriguez-Bunn, Nancy, MS29, 9:30 Mon Sato, Daisuke, MS126, 1:30 Thu Qian, Yuzhou, PP2, 8:30 Wed Rohloff, Martin, MS53, 9:00 Tue Sato, Yuzuru, MS48, 9:00 Tue Qiu, Siwei, MS66, 1:30 Tue Sattari, Sulimon, PP1, 8:30 Tue Quail, Thomas D., MS73, 5:00 Tue Romance, Miguel, MS68, 1:30 Tue Sauer, Timothy, MS15, 2:00 Sun Queirolo, Elena, PP1, 8:30 Tue Romano, David, MS14, 3:00 Sun Sayadi, Taraneh, MS55, 9:30 Tue Quininao, Cristobal, MS74, 5:30 Tue Romeo, Francesco, MS32, 2:15 Mon Schecter, Stephen, MS122, 9:00 Thu Quinn, D Dane, MS133, 1:30 Thu Roque, Antonio C., MS72, 5:30 Tue Rosa, Epaminondas, MS59, 1:30 Tue Scheel, Arnd, MS77, 4:00 Tue R Rosa, Epaminondas, MS72, 4:00 Tue Schelter, Björn, MS115, 9:00 Thu Rachinskiy, Dmitry, MS23, 9:00 Sun Rosa, Epaminondas, MS72, 4:30 Tue Schiff, Steven J., MS109, 4:30 Wed Rachinskiy, Dmitry, MS23, 9:00 Sun Rosado Linares, Jesus, MS29, 10:00 Mon Schmitt, Karl, CP25, 5:05 Mon Rademacher, Jens, MS77, 4:30 Tue Rosato, Anthony, MS39, 1:15 Mon Schumann-Bischoff, Jan, MS61, 3:00 Tue Radons, Gunter, MS10, 9:30 Sun Rosato, Anthony, MS52, 8:30 Tue Schwabedal, Justus T., MS50, 8:30 Tue Radunskaya, Ami, MS34, 1:15 Mon Rosenblum, Michael, MS115, 8:30 Thu Schwartz, Elissa, MS98, 3:00 Wed Rahman, Aminur, MS39, 2:15 Mon Rosenblum, Michael, MS127, 1:30 Thu Schwartz, Ira B., MS33, 1:15 Mon Reagan, Andrew, MS63, 3:00 Tue Schwartz, Ira B., MS33, 1:15 Mon Rosenblum, Michael, MS127, 1:30 Thu Recupero, Vincenzo, MS78, 9:00 Wed Schwarz, Michael, PP2, 8:30 Wed Ross, Shane D., CP6, 5:50 Sun Redner, Sidney, MS105, 4:00 Wed Selvaraj, Prashanth, CP27, 4:20 Tue Rottschafer, Vivi, MS123, 1:30 Thu Redner, Sidney, MS105, 5:30 Wed Sendina Nadal, Irene, MS68, 1:30 Tue Rowley, Clarence, MS60, 1:30 Tue Reimbayev, Reimbay, PP1, 8:30 Tue Sendina Nadal, Irene, MS68, 3:00 Tue Roy, Rajarshi, MS28, 9:30 Mon Reinhardt, Christian P., MS128, 1:30 Seo, Gunog, CP6, 4:50 Sun Thu Roy, Ranadhir, MS97, 5:00 Tue Roy, Subhradeep, PP2, 8:30 Wed Serrano, Sergio, MS119, 1:30 Wed Reinhardt, Christian P., MS128, 1:30 Thu Sewalt, Lotte, MS123, 2:00 Thu Renson, Ludovic, MS121, 9:30 Thu Rubchinsky, Leonid, MS114, 8:30 Thu Shai, Saray, MS102, 2:30 Wed Restrepo, Juan G., MS117, 10:00 Thu Rubchinsky, Leonid, MS114, 8:30 Thu Shaw, Leah, MS33, 1:45 Mon Ribeiro, Ruy M., MS98, 1:30 Wed Rubin, Jonathan E., MS118, 8:30 Thu Shea-Brown, Eric, MS74, 5:00 Tue Riecke, Hermann, CP15, 4:05 Mon Rubin, Jonathan E., MS130, 1:30 Thu Sheombarsing, Ray, PP1, 8:30 Tue Rimbert, Nikolas, MS53, 9:30 Tue Rubin, Jonathan E., MS130, 3:00 Thu Shiferaw, Yohannes, MS126, 2:00 Thu Rink, Bob, MS27, 8:30 Mon Rucklidge, Alastair M., PP1, 8:30 Tue Shilnikov, Andrey, MS116, 10:30 Sun Ritchie, Paul, MS104, 4:30 Wed Ruzzene, Massimo, PD2, 12:00 Tue Shipman, Patrick, MS9, 9:00 Sun Roberts, Andrew, MS36, 1:15 Mon Ryzhov, Evgeny, PP2, 8:30 Wed Shirin, Afroza, CP28, 4:00 Tue

Italicized names indicate session organizers. 2015 SIAM Conference on Applications of Dynamical Systems 241

Shlizeman, Eli, MS7, 10:30 Sun Stremler, Mark A., MS79, 8:30 Wed Teruel, Antonio E., MS118, 10:00 Thu Short, Martin, MS88, 8:30 Wed Stremler, Mark A., MS92, 1:30 Wed Thamara Kunnathu, Shajahan, MS64, Showalter, Kenneth, MS76, 5:00 Tue Stremler, Mark A., MS92, 2:30 Wed 1:30 Tue Sieber, Jan, MS106, 4:30 Wed Strickland, Christopher, MS9, 9:00 Sun Thamara Kunnathu, Shajahan, MS64, 1:30 Tue Siero, Eric, MS123, 2:30 Thu Strickland, Christopher, MS9, 9:00 Sun Thiffeault, Jean-Luc, MS111, 8:30 Thu Signerska, Justyna H., PP2, 8:30 Wed Strogatz, Steven H., CP18, 3:45 Mon Thiffeault, Jean-Luc, MS111, 8:30 Thu Simpson, David J., MS87, 8:30 Wed Stuart, Andrew, IP3, 6:00 Mon Thiffeault, Jean-Luc, MS124, 1:30 Thu Simpson, David J., MS87, 8:30 Wed Sturman, Rob, PP2, 8:30 Wed Thomas, Jim, MS8, 9:30 Sun Simpson, David J., MS100, 1:30 Wed Sudakov, Ivan, MS113, 8:30 Thu Tiedje, Tom, MS113, 10:00 Thu Sinitsyn, Nikolai, MS46, 10:00 Tue Sudakov, Ivan, MS113, 8:30 Thu Tikhomirov, Sergey, MS23, 10:30 Sun Sipahi, Rifat, MS12, 10:30 Sun Suetani, Hiromichi, MS101, 2:30 Wed Timme, Marc, MS54, 9:30 Tue Sivasankaran, Anoop, PP1, 8:30 Tue Sukhinin, Alexey, CP2, 5:10 Sun Timme, Marc, MS115, 8:30 Thu Slawik, Alexander, CP23, 5:05 Mon Sun, Jie, MS5, 8:30 Mon Timme, Marc, MS127, 1:30 Thu Slivinski, Laura, MS63, 1:30 Tue Susuki, Yoshihiko, MS47, 8:30 Tue Titus, Mathew, CP15, 5:05 Mon Slivinski, Laura, MS63, 1:30 Tue Susuki, Yoshihiko, MS60, 1:30 Tue Toenjes, Ralf, MS76, 4:00 Tue So, Paul, MS117, 8:30 Thu Susuki, Yoshihiko, MS60, 3:00 Tue Toenjes, Ralf, MS76, 5:30 Tue So, Paul, MS129, 1:30 Thu Szalai, Robert, MS10, 9:00 Sun Topaz, Chad M., MS40, 2:45 Mon So, Paul, MS129, 2:30 Thu Szalai, Robert, MS121, 8:30 Thu Toroczkai, Zoltan, MS16, 3:30 Sun Solomon, Thomas H., MS26, 8:30 Mon Szalai, Robert, MS133, 1:30 Thu Touboul, Jonathan D., MS66, 1:30 Tue Solomon, Thomas H., MS86, 8:30 Wed Szezech Jr, Jose D., PP1, 8:30 Tue Touboul, Jonathan D., MS74, 4:00 Tue Solomon, Thomas H., MS99, 1:30 Wed Szmolyan, Peter, CP18, 4:45 Mon Touboul, Jonathan D., PP2, 8:30 Wed Sommerlade, Linda, CP27, 5:00 Tue Szwaykowska, Klementyna, MS71, 4:00 Treitman, Yosef M., PP2, 8:30 Wed Sorrentino, Francesco, MS20, 8:30 Mon Tue Tricoche, Xavier M., MS52, 9:30 Tue Sorrentino, Francesco, MS20, 9:30 Mon Szwaykowska, Klementyna, MS71, 5:30 Tue Tsai, Richard, MS69, 3:00 Tue Speetjens, Michel, MS26, 8:30 Mon T Tsimring, Lev S., MS17, 3:00 Sun Speetjens, Michel, MS26, 10:00 Mon Taira, Kunihiko, MS55, 8:30 Tue Tu, Jonathan H., MS42, 1:15 Mon Spiller, Elaine, MS21, 9:00 Mon Talon, Laurent, MS86, 10:00 Wed Tu, Jonathan H., MS42, 1:15 Mon Spinello, Davide, MS30, 9:00 Mon Tang, Wenbo, MS3, 10:00 Sun Tu, Jonathan H., MS55, 8:30 Tue Sridhar, S, MS64, 3:00 Tue Tanwani, Aneel, MS78, 10:00 Wed Turitsyn, Konstantin, MS107, 5:30 Wed Stanton, Samuel, PD2, 12:00 Tue Tao, Molei, MS82, 8:30 Wed Tutberidze, Mikheil, CP20, 4:25 Mon Starke, Jens, MS40, 2:15 Mon Tao, Molei, MS82, 10:00 Wed Tzella, Alexandra, MS86, 9:00 Wed Starosvetsky, Yuli, MS45, 10:00 Tue Tao, Molei, MS95, 1:30 Wed Tzou, Justin C., MS18, 2:30 Sun Starosvetsky, Yuli, MS83, 8:30 Wed Taylor, Dane, MS9, 9:30 Sun Tzou, Justin C., MS81, 8:30 Wed Starosvetsky, Yuli, MS96, 1:30 Wed Taylor, Dane, MS5, 8:30 Mon Tzou, Justin C., MS94, 1:30 Wed Steinbock, Oliver, MS73, 5:30 Tue Taylor-King, Jake P., PP2, 8:30 Wed Steiner, Paul, MS38, 2:15 Mon Teitsworth, Stephen, MS28, 10:00 Mon U Stepan, Gabor, MS10, 9:00 Sun Tel, Tamas, MS58, 1:30 Tue Ueda, Kei-Ichi, CP20, 4:45 Mon Stepan, Gabor, MS10, 10:30 Sun Teramoto, Takashi, PP1, 8:30 Tue Ullah, Ghanim, MS15, 3:30 Sun Stephen Tladi, Maleafisha, CP12, 5:50 Sun Teramura, Toshiki, PP1, 8:30 Tue Ulusoy, Suleyman, CP7, 4:50 Sun Stoica, Cristina, MS79, 9:00 Wed Terra, Maisa O., MS108, 5:30 Wed Uminsky, David T., MS11, 10:00 Sun Uzelac, Ilija, MS126, 3:00 Thu

Italicized names indicate session organizers. 242 2015 SIAM Conference on Applications of Dynamical Systems

V W Wurm, Alexander, MS24, 8:30 Mon Vaidya, Naveen K., MS85, 8:30 Wed Wackerbauer, Renate A., CP16, 4:25 Mon Wurm, Alexander, MS24, 8:30 Mon Vaidya, Naveen K., MS98, 1:30 Wed Wagner, Till, MS113, 9:30 Thu Wyller, John, MS84, 9:00 Wed Vaidya, Naveen K., MS98, 2:30 Wed Wang, Kun, CP7, 5:10 Sun X Vaidya, Umesh, MS131, 2:00 Thu Wang, Wei, MS120, 9:30 Thu Xia, Chao, PP2, 8:30 Wed Vainchtein, Anna, MS83, 8:30 Wed Wang, Xiaosun, MS133, 2:00 Thu Xie, Shuangquan, MS94, 3:00 Wed Vainchtein, Anna, MS96, 1:30 Wed Wang, Xueying, CP27, 4:00 Tue Xing, Tingli, PP1, 8:30 Tue Vainchtein, Dmitri, MS26, 8:30 Mon Wang, Yangyang, MS25, 9:00 Mon Xu, Bin, PP2, 8:30 Wed Wang, Yu V., CP20, 3:45 Mon Vainchtein, Dmitri, MS32, 2:45 Mon Xu, Mu, CP25, 4:25 Mon Vakakis, Alexander, MS32, 1:15 Mon Wang, Zhen, MS68, 1:30 Tue Wang, Zhen, MS68, 2:00 Tue Y Vakakis, Alexander, MS45, 8:30 Tue Yanao, Tomohiro, MS95, 2:30 Wed Wang, Zhen, PP1, 8:30 Tue Vakakis, Alexander, MS45, 8:30 Tue Yanchuk, Serhiy, MS106, 4:00 Wed Warchall, Henry, PD2, 12:00 Tue Van Den Berg, Jan Bouwe, MS56, 8:30 Yang, Dennis, MS84, 8:30 Wed Tue Ward, Michael, MS18, 3:00 Sun Yang, Dennis, MS84, 8:30 Wed Van Den Berg, Jan Bouwe, MS128, 2:00 Thu Ward, Thomas, CP7, 5:30 Sun Yang, Jinkyu, MS83, 8:30 Wed van Heijster, Peter, CP1, 4:30 Sun Wares, Joanna, MS34, 1:15 Mon Ye, Jingxin, MS101, 2:00 Wed van Heijster, Peter, MS70, 1:30 Tue Watanabe, Shinya, PP2, 8:30 Wed Yeaton, Isaac, CP25, 4:45 Mon Watson, Scott T., CP16, 5:05 Mon van Heijster, Peter, MS77, 4:00 Tue Webb, Glenn, MS34, 2:15 Mon Yi, Yanyan, MS126, 1:30 Thu Vandervorst, Robert, MS56, 8:30 Tue Wechselberger, Martin, MS77, 5:30 Tue Yochelis, Arik, MS18, 2:00 Sun Vanneste, Jacques, MS8, 10:30 Sun Wells, Daniel, CP16, 3:45 Mon Yochelis, Arik, MS18, 2:00 Sun Varkonyi, Peter L., MS121, 9:00 Thu Welsh, Andrea J., MS28, 8:30 Mon Yoshimura, Hiroaki, MS4, 9:00 Sun Vasudevan, Ram, MS131, 1:30 Thu Welsh, Andrea J., CP16, 4:45 Mon Young, Alexander L., PP2, 8:30 Wed Vasudevan, Ram, MS131, 3:00 Thu Whitehead, Jared P., MS8, 9:00 Sun Young, Glenn S., PP1, 8:30 Tue Veerman, Frits, CP20, 5:05 Mon Young, Lai-Sang, MS58, 2:00 Tue Wickramasinghe, B.M. Shandeepa D., PP1, Veliz-Cuba, Alan, MS66, 2:00 Tue 8:30 Tue Youngs, Nora, MS14, 3:30 Sun Venel, Juliette, MS91, 1:30 Wed Widiasih, Esther, MS36, 1:15 Mon Verschueren Van Rees, Nicolas, MS18, 3:30 Widiasih, Esther, MS36, 1:45 Mon Z Sun Zakharova, Anna, MS59, 3:00 Tue Vincze, Miklos P., CP12, 4:50 Sun Widiasih, Esther, MS49, 8:30 Tue Zaks, Michael A., MS59, 2:00 Tue Virgin, Lawrie N., CP25, 3:45 Mon Wieczorek, Sebastian M., MS104, 4:00 Zavitz, Daniel R., PP1, 8:30 Tue Wed Virkar, Yogesh, CP16, 4:05 Mon Zelnik, Yuval, CP12, 4:30 Sun Wieczorek, Sebastian M., MS104, 4:00 Wed Vlajic, Nicholas, MS121, 10:00 Thu Zenkov, Dmitry, MS4, 9:00 Sun Wiercigroch, Marian, MS100, 2:30 Wed Vo, Theodore, MS116, 9:00 Sun Zenkov, Dmitry, MS22, 10:00 Mon Williams, Matthew O., MS60, 2:00 Tue Vo, Theodore, MS116, 9:00 Sun Zhang, Calvin, CP27, 5:20 Tue Wilson, Dan D., MS109, 4:00 Wed Volkening, Alexandria, MS40, 1:15 Mon Zhang, Fumin, MS3, 9:30 Sun Wilson, Dan D., MS109, 4:00 Wed Volkening, Alexandria, MS40, 1:15 Mon Zhang, Yijing, MS96, 2:30 Wed Wodarz, Dominik, MS34, 2:45 Mon Vollmer, Jürgen, MS53, 8:30 Tue Zhang, Zhihui, CP20, 4:05 Mon Wojcik, Jeremy, MS50, 9:30 Tue Vollmer, Jürgen, MS53, 8:30 Tue Zhao, Lihong, CP27, 4:40 Tue Wojcik, Jeremy, PP2, 8:30 Wed Volper, Vladimir, MS97, 4:00 Tue Zhou, Douglas, MS7, 9:00 Sun Worthington, Joachim, PP1, 8:30 Tue von Brecht, James, MS88, 9:00 Wed Zhou, Douglas, MS7, 10:00 Sun Wu, Hao, MS52, 9:00 Tue Zhu, Xueyu, MS90, 9:00 Wed Wu, Qiliang, MS19, 8:30 Mon

Italicized names indicate session organizers. 2015 SIAM Conference on Applications of Dynamical Systems 243

Zhuzhoma, Evgeny, PP2, 8:30 Wed Zlotnik, Anatoly, MS30, 10:00 Mon Zochowski, Michal, MS127, 3:00 Thu Zykov, Vladimir, MS93, 2:00 Wed

Italicized names indicate session organizers. 244 2015 SIAM Conference on Applications of Dynamical Systems

Notes 2015 SIAM Conference on Applications of Dynamical Systems 245

DS15 Budget

Conference Budget SIAM Conference on Dynamical Systems May 17 - 21, 2015 Snowbird, UT

Expected Paid Attendance 780

Revenue Registration Income $223,355 Total $223,355

Expenses Printing $9,200 Organizing Committee $6,500 Invited Speakers $20,000 Food and Beverage $35,800 AV Equipment and Telecommunication $10,800 Advertising $7,000 Conference Labor (including benefits) $56,846 Other (supplies, staff travel, freight, misc.) $19,400 Administrative $18,578 Accounting/Distribution & Shipping $9,907 Information Systems $17,862 Customer Service $6,747 Marketing $10,597 Office Space (Building) $6,703 Other SIAM Services $7,079 Total $243,019

Net Conference Expense ($19,664)

Support Provided by SIAM $19,664 $0

Estimated Support for Travel Awards not included above:

Early Career and Students 67 $50,550

246 Snowbird Ski and Summer2015 SIAM Resort, Conference Hotel on Applications Floor of DynamicalPlan Systems

Snowbird Cliff Lodge Level B

Snowbird Cliff Lodge Level C

FSC logo text box indicating size & layout of logo. Conlins to insert logo.