Crises, Sudden Changes in Chaotic Attractors, and Transient Chaos
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Chaotic Advection, Diffusion, and Reactions in Open Flows Tamás Tél, György Károlyi, Áron Péntek, István Scheuring, Zoltán Toroczkai, Celso Grebogi, and James Kadtke
Chaotic advection, diffusion, and reactions in open flows Tamás Tél, György Károlyi, Áron Péntek, István Scheuring, Zoltán Toroczkai, Celso Grebogi, and James Kadtke Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science 10, 89 (2000); doi: 10.1063/1.166478 View online: http://dx.doi.org/10.1063/1.166478 View Table of Contents: http://scitation.aip.org/content/aip/journal/chaos/10/1?ver=pdfcov Published by the AIP Publishing This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.173.125.76 On: Mon, 24 Mar 2014 14:44:01 CHAOS VOLUME 10, NUMBER 1 MARCH 2000 Chaotic advection, diffusion, and reactions in open flows Tama´sTe´l Institute for Theoretical Physics, Eo¨tvo¨s University, P.O. Box 32, H-1518 Budapest, Hungary Gyo¨rgy Ka´rolyi Department of Civil Engineering Mechanics, Technical University of Budapest, Mu¨egyetem rpk. 3, H-1521 Budapest, Hungary A´ ron Pe´ntek Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238 Istva´n Scheuring Department of Plant Taxonomy and Ecology, Research Group of Ecology and Theoretical Biology, Eo¨tvo¨s University, Ludovika te´r 2, H-1083 Budapest, Hungary Zolta´n Toroczkai Department of Physics, University of Maryland, College Park, Maryland 20742-4111 and Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435 Celso Grebogi Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 James Kadtke Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238 ͑Received 30 July 1999; accepted for publication 8 November 1999͒ We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. -
CURRICULUM VITA Edward Ott Distinguished University Professor of Electrical Engineering and of Physics
CURRICULUM VITA Edward Ott Distinguished University Professor of Electrical Engineering and of Physics I. Personal Data: Date and Place of Birth: Dec. 22, 1941, New York City, NY Home Address: 12421 Borges Ave., Silver Spring, MD 20904 Work Address: Institute for Plasma Research University of Maryland College Park, MD 20472 Work Telephone: (301)405-5033 II. Education: B.S. (1963), Electrical Engineering, The Cooper Union. M.S. (1965), Electrophysics, Polytechnic University. Ph.D. (1967), Electrophysics, Polytechnic University. III. Experience: 1967-1968 NSF Postdoctoral Fellow, Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, U.K. 1968-1979 Faculty of the Department of Electrical Engineering, Cornell University, Ithaca, NY. 1976 and Plasma Physics Division, Naval Research 1971-1972 Laboratory, Washington, D.C. 1985 Institute for Theoretical Physics, University of California, Santa Barbara, CA. 1979-Present Department of Physics and Department of Electrical Engineering, University of Maryland, College Park, MD. (Ott–2) IV. Professional Activities: Fellow, American Physical Society. Fellow, IEEE. Fellow, World Innovation Foundation. Listed in the Highly Cited Researchers Database of the ISI. Associate Editor, Physics of Fluids (1977–1979). Correspondent, Comments on Plasma Physics (1983–1993). Board of Editors, Physical Review A (1986–1988). Divisional Associate Editor, Physical Review Letters (1989–1993). Editor of Special Issue of Chaos on Chaotic Scattering (1993). Advisory Board, Chaos: An Interdisciplinary Journal of Nonlinear Science (1991–2000). Editorial Board, Chaos: An Interdisciplinary Journal of Nonlinear Science (2000–2003). Editorial Board, Dynamics and Stability of Systems (1995–2000). Editorial Board, Central European Journal of Physics (2002–present). Editor, Physica D: Nonlinear Phenomena (1999–2002). -
Table of Contents (Print, Part 2)
PERIODICALS PHYSICAL REVIEW E Postmaster send address changes to: For editorial and subscription correspondence, APS Subscription Services please see inside front cover Suite 1NO1 „ISSN: 1539-3755… 2 Huntington Quadrangle Melville, NY 11747-4502 THIRD SERIES, VOLUME 75, NUMBER 6 CONTENTS JUNE 2007 PART 2: STATISTICAL AND NONLINEAR PHYSICS, FLUID DYNAMICS, AND RELATED TOPICS RAPID COMMUNICATIONS Chaos and pattern formation Giant acceleration in slow-fast space-periodic Hamiltonian systems (4 pages) ........................... 065201͑R͒ D. V. Makarov and M. Yu. Uleysky Controlling spatiotemporal chaos using multiple delays (4 pages) ..................................... 065202͑R͒ Alexander Ahlborn and Ulrich Parlitz Signatures of fractal clustering of aerosols advected under gravity (4 pages) ............................ 065203͑R͒ Rafael D. Vilela, Tamás Tél, Alessandro P. S. de Moura, and Celso Grebogi Fluid dynamics Clustering of matter in waves and currents (4 pages) ............................................... 065301͑R͒ Marija Vucelja, Gregory Falkovich, and Itzhak Fouxon Experimental study of the bursting of inviscid bubbles (4 pages) ..................................... 065302͑R͒ Frank Müller, Ulrike Kornek, and Ralf Stannarius Surface thermal capacity and its effects on the boundary conditions at fluid-fluid interfaces (4 pages) ....... 065303͑R͒ Kausik S. Das and C. A. Ward Plasma physics Direct evidence of strongly inhomogeneous energy deposition in target heating with laser-produced ion beams (4 pages) .................................................................................. -
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems Wen-Xu Wanga;b, Ying-Cheng Laic;d;e, and Celso Grebogie a School of Systems Science, Beijing Normal University, Beijing, 100875, China b Business School, University of Shanghai for Science and Technology, Shanghai 200093, China c School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA d Department of Physics, Arizona State University, Tempe, Arizona 85287, USA e Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE, UK Wen-Xu Wang, Ying-Cheng Lai, and Celso Grebogi 1 Abstract The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space re- construction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, under- stand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these tasks, especially prediction and control, an accurate reconstruction of the original system is required. -
Chaos Theory: the Essential for Military Applications
U.S. Naval War College U.S. Naval War College Digital Commons Newport Papers Special Collections 10-1996 Chaos Theory: The Essential for Military Applications James E. Glenn Follow this and additional works at: https://digital-commons.usnwc.edu/usnwc-newport-papers Recommended Citation Glenn, James E., "Chaos Theory: The Essential for Military Applications" (1996). Newport Papers. 10. https://digital-commons.usnwc.edu/usnwc-newport-papers/10 This Book is brought to you for free and open access by the Special Collections at U.S. Naval War College Digital Commons. It has been accepted for inclusion in Newport Papers by an authorized administrator of U.S. Naval War College Digital Commons. For more information, please contact [email protected]. The Newport Papers Tenth in the Series CHAOS ,J '.' 'l.I!I\'lt!' J.. ,\t, ,,1>.., Glenn E. James Major, U.S. Air Force NAVAL WAR COLLEGE Chaos Theory Naval War College Newport, Rhode Island Center for Naval Warfare Studies Newport Paper Number Ten October 1996 The Newport Papers are extended research projects that the editor, the Dean of Naval Warfare Studies, and the President of the Naval War CoJIege consider of particular in terest to policy makers, scholars, and analysts. Papers are drawn generally from manuscripts not scheduled for publication either as articles in the Naval War CollegeReview or as books from the Naval War College Press but that nonetheless merit extensive distribution. Candidates are considered by an edito rial board under the auspices of the Dean of Naval Warfare Studies. The views expressed in The Newport Papers are those of the authors and not necessarily those of the Naval War College or the Department of the Navy. -
Strange Attractors That Are Not Chaotic
Physica 13D (1984) 261-268 North-Holland, Amsterdam STRANGE ATTRACTORS THAT ARE NOT CHAOTIC Celso GREBOGI, a Edward OTT, ~b Steven PELIKAN, c and James A. YORKE d Received 7. February 1984 It is shown that in certain types of dynamical systems it is possible to have attractors which are strange but not chaotic. Here we use the word strange to refer to the geometry or shape of the attracting set, while the word chaotic refers to the dynamics of orbits on the attractor (in particular, the exponential divergence of nearby trajectories). We first give examples for which it can be demonstrated that there is a strange nonchaotic attractor. These examples apply to a class of maps which model nonlinear oscillators (continuous time) which are externally driven at two incommensurate frequencies. It is then shown that such attractors are persistent under perturbations which preserve the original system type (i.e., there are two incommensurate external driving frequencies). This suggests that, for systems of the type which we have considered, nonchaotic strange attractors may be expected to occur for a finite interval of parameter values. On the other hand, when small perturbations which do not preserve the system type are numerically introduced the strange nonchaotic attractor is observed to be converted to a periodic or chaotic orbit. Thus we conjecture that, in general, continuous time systems (" flows") which are not externally driven at two incommensurate frequencies should not be expected to have strange nonchaotic attractors except possibly on a set of measure zero in the parameter space. 1. Introduction and definitions ties [1] such as noninteger fractal dimension, Cantor set structure, or nowhere differentiability. -
CURRICULUM VITAE Edward Ott Distinguished University Professor
Ott-1 CURRICULUM VITAE Edward Ott Distinguished University Professor of Electrical Engineering and of Physics Work Address: Institute for Research in Electronics and Applied Physics University of Maryland 8279 Paint Branch Drive College Park, MD 20742-3511 Work Telephone: 301-405-5033 I. Education: B.S. 1963 Electrical Engineering, The Cooper Union M.S. 1965 Electrophysics, Polytechnic University Ph.D. 1967 Electrophysics, Polytechnic University II. Experience 1967-1968 NSF Postdoctoral Fellow Department of Applied Mathematics and Theoretical Physics Cambridge University, Cambridge, U.K. 1968-1979 Faculty of the Department of Electrical Engineering Cornell University, Ithaca, NY 1976 and Plasma Physics Division 1971-1972 Naval Research Laboratory, Washington, D.C. 1985 Institute for Theoretical Physics University of California Santa Barbara, CA 1979-Present Department of Electrical and Computer Engineering, and Department of Physics University of Maryland, College Park, MD III. Publications Ott-2 Professor Ott is an author of over 450 papers in refereed scientific journals. He is the author of the book Chaos in Dynamical Systems (Cambridge University Press), a graduate level textbook also widely used by researchers in the field (over 6000 Google Scholar citations) and an editor of the book Coping with Chaos (John Wiley). According to Google Scholar, Prof. Ott has received over 58,600 citations and has an h- index of 109. According to the ISI Web of Science, Prof. Ott’s journal articles have received over 33,800 citations with a corrosponding h-index of 91. (Note: For these citation and h- index data, papers have been filtered out if they list E.Ott as an author, but the E. -
Fourth SIAM Conference on Applications of Dynamical Systems
Utah State University DigitalCommons@USU All U.S. Government Documents (Utah Regional U.S. Government Documents (Utah Regional Depository) Depository) 5-1997 Fourth SIAM Conference on Applications of Dynamical Systems SIAM Activity Group on Dynamical Systems Follow this and additional works at: https://digitalcommons.usu.edu/govdocs Part of the Physical Sciences and Mathematics Commons Recommended Citation Final program and abstracts, May 18-22, 1997 This Other is brought to you for free and open access by the U.S. Government Documents (Utah Regional Depository) at DigitalCommons@USU. It has been accepted for inclusion in All U.S. Government Documents (Utah Regional Depository) by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. tI...~ Confers ~'t' '"' \ 1I~c9 ~ 1'-" ~ J' .. c "'. to APPLICAliONS cJ May 18-22, 1997 Snowbird Ski and Summer Resort • Snowbird, Utah Sponsored by SIAM Activity Group on Dynamical Systems Conference Themes The themes of the 1997 conference will include the following topics. Principal Themes: • Dynamics in undergraduate education • Experimental studies of nonlinear phenomena • Hamiltonian systems and transport • Mathematical biology • Noise in dynamical systems • Patterns and spatio-temporal chaos Applications in • Synchronization • Aerospace engineering • Biology • Condensed matter physics • Control • Fluids • Manufacturing • Me;h~~~~nograPhY 19970915 120 • Lasers and o~ • Quantum UldU) • 51a m.@ Society for Industrial and Applied Mathematics http://www.siam.org/meetingslds97/ds97home.htm 2 " DYNAMICAL SYSTEMS Conference Prl Contents A Message from the Conference Chairs ... Get-Togethers 2 Dear Colleagues: Welcoming Message 2 Welcome to Snowbird for the Fourth SIAM Conference on Applications of Dynamica Systems. Organizing Committee 2 This highly interdisciplinary meeting brings together a diverse group of mathematicians Audiovisual Notice 2 scientists, and engineers, all working on dynamical systems and their applications. -
Final State Sensitivity: an Obstruction to Predictability
Volume 99A, number 9 PHYSICS LETTERS 26 December 1983 FINAL STATE SENSITIVITY: AN OBSTRUCTION TO PREDICTABILITY Celso GREBOGI 1 Steven W. McDONALD 1 , Edward OTT 1'2 and James A. YORKE 3 University of Maryland, College Park, MD 20742, USA Received 21 October 1983 It is shown that nonlinear systems with multiple attractors commonly require very accurate initial conditions for the reliable prediction of final states. A scaling exponent for the final-state-uncertain phase space volume dependence on un- certainty in initial conditions is defined and related to the fractai dimension of basin boundaries. Typical nonlinear dynamical systems may have more is the "basin bounctary". It the initial conaitions are than one possible time-asymptotic final state. In such uncertain by an amount e, then (cf. fig. 1), for those cases the final state that is eventually reached depends initial conditions within e of the boundary, we cannot on the initial state of the system. In this letter we say a priori to which attractor the orbit eventually wish to consider the extent to which uncertainty in tends. For example, in fig. 1, 1 and 2 represent two initial conditions leads to uncertainty in the final state. initial conditions with an uncertainty e. The orbit To orient the discussion, consider the simple two- generated by initial condition 1 is attracted to attrac- dimensional phase space diagram schematically de- tor B. Initial condition 2, however, is uncertain in the picted in fig. 1. There are two possible final states sense that the orbit generated by 2 may be attracted ("attractors") denoted A and B. -
Machine Learning for Analysis of High-Dimensional Chaotic Spatiotemporal Dynamical Systems
MACHINE LEARNING FOR ANALYSIS OF HIGH-DIMENSIONAL CHAOTIC SPATIOTEMPORAL DYNAMICAL SYSTEMS 6th December 2018 Princeton Plasma Physics Laboratory Theory Seminar Jaideep Pathak Zhixin Lu, Alex Wikner, Rebeckah Fussell, Brian Hunt, Michelle Girvan, Edward Ott University of Maryland, College Park Given some data from a dynamical system, what can we say about the dynamical process that generated this data? !2 OUTLINE Short-term forecasting Prediction Given a limited time series of past measurements can we predict the future state of the dynamical system, at least in the short term? Reconstructing the attractor Long-term Can we learn something about the long-term dynamics of the dynamics system? Specifically, can we use our setup to understand the ergodic properties of a high-dimensional dynamical system? Scalability Can we use our setup for very high-dimensional attractors? Large systems !3 INTRODUCTION Operationally, we say a x1(t) − x2(t) = δx(t) dynamical system is chaotic if, in a ∥δx(t)∥ ∼ ∥δx(0)∥ exp(Λt) bounded phase space, two nearby trajectories diverge exponentially. !4 INTRODUCTION In a chaotic system, a perturbation to the trajectory may be stable (contracting) in some directions, unstable (expanding) in some directions. !5 INTRODUCTION This leads to the concept of a spectrum of ‘Lyapunov exponents’. The exponential rates of growth (or contraction) of perturbations in different directions are characterized by corresponding Lyapunov exponents. !6 INTRODUCTION The Lyapunov exponents of a dynamical system are an important characteristic and provide us with a lot of useful information. What is the ‘complexity’? Is a system chaotic? of the system What is the effective dimension of the chaotic What is the possible attractor of the system prediction horizon? (via the ‘Kaplan-Yorke conjecture’)? !7 INTRODUCTION In general, in the past it has proven difficult (and sometimes not possible) to estimate the spectrum of Lyapunov exponents of a dynamical system purely from limited time series data. -
Data Based Identification and Prediction of Nonlinear And
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems Wen-Xu Wanga;b, Ying-Cheng Laic;d;e, and Celso Grebogie a School of Systems Science, Beijing Normal University, Beijing, 100875, China b Business School, University of Shanghai for Science and Technology, Shanghai 200093, China c School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA d Department of Physics, Arizona State University, Tempe, Arizona 85287, USA e Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE, UK arXiv:1704.08764v1 [physics.data-an] 27 Apr 2017 Wen-Xu Wang, Ying-Cheng Lai, and Celso Grebogi 1 Abstract The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space re- construction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, under- stand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. -
Introduction to Focus Issue: When Machine Learning Meets Complex Systems: Networks, Chaos, and Nonlinear Dynamics
Introduction to Focus Issue: When machine learning meets complex systems: Networks, chaos, and nonlinear dynamics Cite as: Chaos 30, 063151 (2020); https://doi.org/10.1063/5.0016505 Submitted: 04 June 2020 . Accepted: 05 June 2020 . Published Online: 26 June 2020 Yang Tang , Jürgen Kurths , Wei Lin , Edward Ott, and Ljupco Kocarev COLLECTIONS Paper published as part of the special topic on When Machine Learning Meets Complex Systems: Networks, Chaos and Nonlinear Dynamics Note: This paper is part of the Focus Issue, “When Machine Learning Meets Complex Systems: Networks, Chaos and Nonlinear Dynamics.” ARTICLES YOU MAY BE INTERESTED IN Recurrence analysis of slow–fast systems Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 063152 (2020); https:// doi.org/10.1063/1.5144630 Reducing network size and improving prediction stability of reservoir computing Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 063136 (2020); https:// doi.org/10.1063/5.0006869 Detecting causality from time series in a machine learning framework Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 063116 (2020); https:// doi.org/10.1063/5.0007670 Chaos 30, 063151 (2020); https://doi.org/10.1063/5.0016505 30, 063151 © 2020 Author(s). Chaos ARTICLE scitation.org/journal/cha Introduction to Focus Issue: When machine learning meets complex systems: Networks, chaos, and nonlinear dynamics Cite as: Chaos 30, 063151 (2020); doi: 10.1063/5.0016505 Submitted: 4 June 2020 · Accepted: 5 June 2020 · Published Online: 26 June 2020 View Online Export