15Th Conference on DYNAMICAL SYSTEMS Theory and Applications DSTA 2019 ABSTRACTS
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Intermittency Induced in a Bistable Multiscroll Attractor by Means of Stochastic Modulation
CYBERNETICS AND PHYSICS, VOL. 8, NO. 3, 2019, 114–120 INTERMITTENCY INDUCED IN A BISTABLE MULTISCROLL ATTRACTOR BY MEANS OF STOCHASTIC MODULATION Jose´ L. Echenaus´ıa-Monroy Guillermo Huerta-Cuellar∗ Laboratory of Dynamical Systems Laboratory of Dynamical Systems CULagos, Universidad de Guadalajara CULagos, Universidad de Guadalajara Mexico´ Mexico´ [email protected] ∗Corresponding author: [email protected] Rider Jaimes-Reategui´ Juan H. Garc´ıa-Lopez´ Hector´ E. Gilardi-Velazquez´ Laboratory of Dynamical Systems Laboratory of Dynamical Systems Facultad de Ingenier´ıa CULagos, Universidad de CULagos, Universidad de Universidad Panamericana Guadalajara, Mexico´ Guadalajara, Mexico´ Mexico´ [email protected] [email protected] [email protected] Article history: Received 16.10.2019, Accepted 26.11.2019 Abstract inverse period-doubling bifurcations, respectively, and In this work, numerical results of a nonlinear switch- crisis-induced intermittency with a crisis of chaotic at- ing system that presents bistable attractors subjected to tractors [Manneville & Pomeau, 1979; Hirsh, Nauen- stochastic modulation are shown. The system exhibits a berg, & Scalpino , 1982; Hirsh, Huberman, & Scalpino; dynamical modification of the bistable attractor, giving Hu, & Rudnick]. For systems that show multistable be- rise to an intermit behavior, which depends of modula- havior, noise presence can be useful to influence inter- tion strength. The resulting attractor converge to an in- esting dynamics as hopping attractor [Kraut, & Feudel; termittent double-scroll, for low amplitude modulation, Huerta-Cuellar et. al.; Pisarchik et. al.], as physical and and a 9-scroll attractor for a higher applied noise ampli- natural phenomenons [Huerta-Cuellar et. al.; Pisarchik tude. A Detrended Fluctuation Analysis (DFA) applied et. -
Notices of the American Mathematical Society June/July 2006
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Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System
Hindawi Complexity Volume 2020, Article ID 8175639, 17 pages https://doi.org/10.1155/2020/8175639 Research Article Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System Qiang Lai ,1 Paul Didier Kamdem Kuate ,2 Huiqin Pei ,1 and Hilaire Fotsin 2 1School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China 2Laboratory of Condensed Matter, Electronics and Signal Processing Department of Physics, University of Dschang, P.O. Box 067, Dschang, Cameroon Correspondence should be addressed to Qiang Lai; [email protected] Received 17 January 2020; Revised 18 February 2020; Accepted 26 February 2020; Published 28 March 2020 Guest Editor: Chun-Lai Li Copyright © 2020 Qiang Lai et al. *is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. *is paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. *e circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method. 1. Introduction system may generate hidden attractor. Also, a lot of pre- vious studies have shown that chaotic systems with mul- Encouraging progress has been made on chaos in the past tiple unstable equilibria usually have richer dynamic few decades. -
Quantum-Inspired Identification of Complex Cellular Automata
Quantum-inspired identification of complex cellular automata Matthew Ho,1, 2, ∗ Andri Pradana,1, y Thomas J. Elliott,3, 2, 1, z Lock Yue Chew,1, 2, x and Mile Gu1, 2, 4, { 1School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore 2Complexity Institute, Nanyang Technological University, Singapore 637335, Singapore 3Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom 4Centre for Quantum Technologies. National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore (Dated: March 29, 2021) Elementary cellular automata (ECA) present iconic examples of complex systems. Though de- scribed only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex dynamics capable of universal computation. Yet, the classification of precisely which rules exhibit complex behaviour remains a significant challenge. Here we approach this question using tools from quantum stochastic modelling, where quantum statistical memory { the memory required to model a stochastic process using a class of quantum machines { can be used to quantify the structure of a stochastic process. By viewing ECA rules as transformations of stochastic patterns, we ask: Does an ECA generate structure as quantified by the quantum statistical memory, and if so, how quickly? We illustrate how the growth of this measure over time correctly distinguishes simple ECA from complex counterparts. Moreover, it provides a more refined means for quantitatively identifying complex ECAs { providing a spectrum on which we can rank the complexity of ECA by the rate in which they generate structure. t-1 We all have some intuition of complexity. -
Kaotik Sistemlerin Klasik Ve Zeki Yaklaşimlar Ile Kontrolü
T.C. SAKARYA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ KAOTİK SİSTEMLERİN KLASİK VE ZEKİ YAKLAŞIMLAR İLE KONTROLÜ DOKTORA TEZİ Uğur Erkin KOCAMAZ Enstitü Anabilim Dalı : ELEKTRİK-ELEKTRONİK MÜHENDİSLİĞİ Enstitü Bilim Dalı : ELEKTRONİK Tez Danışmanı : Doç. Dr. Yılmaz UYAROĞLU Kasım 2018 T.C. SAKARYA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ KAOTİK SİSTEMLERİN KLASİK VE ZEKİ YAKLAŞIMLAR İLE KONTROLÜ DOKTORA TEZİ Uğur Erkin KOCAMAZ Enstitü Anabilim Dalı : ELEKTRİK-ELEKTRONİK MÜHENDİSLİĞİ Enstitü Bilim Dalı : ELEKTRONİK BEYAN Tez içindeki tüm verilerin akademik kurallar çerçevesinde tarafımdan elde edildiğini, görsel ve yazılı tüm bilgi ve sonuçların akademik ve etik kurallara uygun şekilde sunulduğunu, kullanılan verilerde herhangi bir tahrifat yapılmadığını, başkalarının eserlerinden yararlanılması durumunda bilimsel normlara uygun olarak atıfta bulunulduğunu, tezde yer alan verilerin bu üniversite veya başka bir üniversitede herhangi bir tez çalışmasında kullanılmadığını beyan ederim. Uğur Erkin KOCAMAZ 07.11.2018 TEŞEKKÜR Bu çalışmanın ortaya çıkmasında bana yardımcı olan, ilgi ve desteğini hiç eksiltmeyen, yol gösterici olan, fikirlerime önem veren, engin bilgi ve tecrübesiyle beni yönlendiren değerli danışmanım Doç. Dr. Yılmaz UYAROĞLU’na teşekkür ederim. Benim bu aşamaya gelmemde en çok emeği geçen, her zaman maddi ve manevi desteklerini arkamda hissettiğim annem babam Cemile ve Numan KOCAMAZ’a ve kardeşim Çiğdem ALTUN’a en içten saygı, sevgi ve şükranlarımı sunarım. i İÇİNDEKİLER TEŞEKKÜR ..……………………………………………………………………… i İÇİNDEKİLER ………………………………………………………………….... -
Quantum Versus Classical Measures of Complexity on Classical Information
Quantum versus Classical Measures of Complexity on Classical Information Lock Yue Chew, PhD Division of Physics and Applied Physics School of Physical & Mathematical Sciences & Complexity Institute Nanyang Technological University Astronomical Scale Macroscopic Scale Mesoscopic Scale What is Complexity? • Complexity is related to “Pattern” and “Organization”. Nature inherently organizes; Pattern is the fabric of Life. James P. Crutchfield • There are two extreme forms of Pattern: generated by a Clock and a Coin Flip. • The former encapsulates the notion of Determinism, while the latter Randomness. • Complexity is said to lie between these extremes. J. P. Crutchfield and K. Young, Physical Review Letters 63, 105 (1989). Can Complexity be Measured? • To measure Complexity means to measure a system’s structural organization. How can that be done? • Conventional Measures: • Difficulty in Description (in bits) – Entropy; Kolmogorov-Chaitin Complexity; Fractal Dimension. • Difficulty in Creation (in time, energy etc.) – Computational Complexity; Logical Depth; Thermodynamic Depth. • Degree of organization – Mutual Information; Topological ϵ- machine; Sophistication. S. Lloyd, “Measures of Complexity: a Non-Exhaustive List”. Topological Ɛ-Machine 1. Optimal Predictor of the System’s Process 2. Minimal Representation – Ockham’s Razor 3. It is Unique. 4. It gives rise to a new measure of Complexity known as Statistical Complexity to account for the degree of organization. 5. The Statistical Complexity has an essential kind of Representational Independence. J. P. Crutchfield, Nature 8, 17 (2012). Concept of Ɛ-Machine Symbolic Sequences: ….. S-2S-1S0S1 ….. Futures : Past : • Within each partition, we have Partitioning the set 푺 of all histories into causal states 푆푖. where 푠 and 푠′ are two different individual histories in the same partition. -
Itinerary Synchronization Between PWL Systems Coupled with Unidirectional Links
Itinerary synchronization between PWL systems coupled with unidirectional links A. Anzo-Hern´andeza, E. Campos-Cant´onb∗ and Matthew Nicolc aC´atedrasCONACYT - Benem´eritaUniversidad Aut´onoma de Puebla, Facultad de Ciencias F´ısico-Matematicas,´ Benemerita´ Universidad Autonoma´ de Puebla, Avenida San Claudio y 18 Sur, Colonia San Manuel, 72570. Puebla, Puebla, Mexico.´ [email protected] bDivision´ de Matematicas´ Aplicadas, Instituto Potosino de Investigaci´onCient´ıficay Tecnol´ogicaA.C. Camino a la Presa San Jose´ 2055 col. Lomas 4a Seccion,´ 78216, San Luis Potos´ı, SLP, Mexico.´ [email protected],∗Corresponding author. cMathematics Department, University of Houston, Houston, Texas, 77204-3008, USA. [email protected]. 1 Abstract 2 In this paper the collective dynamics of N-coupled piecewise linear 3 (PWL) systems with different number of scrolls is studied. The cou- 4 pling is in a master-slave sequence configuration, with this type of cou- 5 pling we investigate the synchrony behavior of a ring-connected network 6 and a chain-connected network both with unidirectional links. Itinerary 7 synchronization is used to detect synchrony behavior. Itinerary synchro- 8 nization is defined in terms of the symbolic dynamics arising by assigning 9 different numbers to the regions where the scrolls are generated. A weaker 10 variant of this notion, -itinerary synchronization is also introduced and 11 numerically investigated. It is shown that in certain parameter regimes 12 if the inner connection between nodes takes account of all the state vari- 13 ables of the system (by which we mean that the inner coupling matrix 14 is the identity matrix), then itinerary synchronization occurs and the co- 15 ordinate motion is determined by the node with the smallest number of 16 scrolls. -
Coexistence of Attractors in Integer- and Fractional-Order
Pramana – J. Phys. (2019) 93:12 © Indian Academy of Sciences https://doi.org/10.1007/s12043-019-1786-3 Coexistence of attractors in integer- and fractional-order three-dimensional autonomous systems with hyperbolic sine nonlinearity: Analysis, circuit design and combination synchronisation SIFEU TAKOUGANG KINGNI1, JUSTIN ROGER MBOUPDA PONE2,∗, GAETAN FAUTSO KUIATE3 and VIET-THANH PHAM4,5 1Department of Mechanical, Petroleum and Gas Engineering, Faculty of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon 2Department of Electrical Engineering, Fotso Victor University Institute of Technology (IUT-FV), University of Dschang, P.O. Box 134, Bandjoun, Cameroon 3Department of Physics, Higher Teacher Training College, University of Bamenda, P.O. Box 39, Bamenda, Cameroon 4Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong District, Hanoi 100000, Vietnam 5Phenikaa Research and Technology Institute (PRATI), A&A Green Phoenix Group, 167 Hoang Ngan, Hanoi 100000, Vietnam ∗Corresponding author. E-mail: [email protected] MS received 23 August 2018; revised 7 December 2018; accepted 13 December 2018; published online 8 May 2019 Abstract. This paper reports the results of the analytical, numerical and analogical analyses of integer- and fractional-order chaotic systems with hyperbolic sine nonlinearity (HSN). By varying a parameter, the integer order of the system displays transcritical bifurcation and new complex shapes of bistable double-scroll chaotic attractors and four-scroll chaotic attractors. The coexistence among four-scroll chaotic attractors, a pair of double-scroll chaotic attractors and a pair of point attractors is also reported for specific parameter values. Numerical results indicate that commensurate and incommensurate fractional orders of the systems display bistable double-scroll chaotic attractors, four-scroll chaotic attractors and coexisting attractors between a pair of double-scroll chaotic attractors and a pair of point attractors. -
Editorial Complexity, Dynamics, Control, and Applications of Nonlinear Systems with Multistability
Hindawi Complexity Volume 2020, Article ID 8510930, 7 pages https://doi.org/10.1155/2020/8510930 Editorial Complexity, Dynamics, Control, and Applications of Nonlinear Systems with Multistability Viet-Thanh Pham ,1,2,3 Sundarapandian Vaidyanathan ,4 and Tomasz Kapitaniak3 1Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong District, Hanoi 100000, Vietnam 2Phenikaa Research and Technology Institute (PRATI), A&A Green Phoenix Group, 167 Hoang Ngan, Hanoi 100000, Vietnam 3Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, Lodz 90-924, Poland 4Research and Development Centre, Vel Tech University, No. 42, Avadi-Vel Tech Road, Avadi, Chennai, Tamil Nadu 600062, India Correspondence should be addressed to Viet-anh Pham; [email protected] Received 4 June 2020; Accepted 5 June 2020; Published 4 September 2020 Copyright © 2020 Viet-anh Pham et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Multistability is a critical property of nonlinear dynamical complex and challenging task. Furthermore, circuit reali- systems, where a variety of phenomena such as coexisting zations (simulations and hardware design) of multistable attractors can appear for the same parameters but with systems are useful for various practical applications in different initial conditions. e flexibility in the system’s engineering. performance can be achieved without changing parameters. is special issue aims to introduce and discuss novel Complex dynamics have been observed in multistable sys- results, control techniques, and circuit simulations for tems, and we have witnessed systems with multistability in complex nonlinear systems with multistability. -
IPS Meeting 2015 4 - 6 March
IPS Meeting 2015 4 - 6 March Institute of Physics Singapore Conference Program (post-printed version, status: March 3, 2015, 17:00SGT) The IPS Meeting 2015 thanks its sponsors for their generous support Institutional Sponsors: SINGAPORE UNIVERSITY OF TECHNOLOGY AND DESIGN Established in collaboration with MIT 1 Foreword Dear fellow Physicists, this year we are back again to the School of Physical and Mathematical Sciences on the campus of Nanyang Technological University for our annual gathering of physicists active in research. For some of our colleagues, who come from their new campus of the Singapore University of Technology and Design (SUTD), this is probably as far as it gets - at least in Singapore. Some time ago, when the IPS council got together, we realized that the UNESCO had declared 2015 as the international year of light. As physicists, this is something many of us use in their daily work, so here was the theme for this year’s meeting. We felt that a focus session on precision measurements and Spectroscopy does fit very well this theme - and a lot of work is done on this topic in Singapore as well! This emphasis is also highlighted by plenary talks discussing exciting new developments in various realizations of precision measurements. It turned out that even one of our colleagues who works – among other topics – on black holes got noted widely for his work describing light paths around these objects - something that made it into a major Hollywood movie. So convinced Edward Teo to open the meeting with a plenary talk, explaining to us the exotic physics hidden in the movie. -
A Memristive Hyperchaotic Multiscroll Jerk System with Controllable Scroll Numbers
June 20, 2017 15:16 WSPC/S0218-1274 1750091 International Journal of Bifurcation and Chaos, Vol. 27, No. 6 (2017) 1750091 (15 pages) c World Scientific Publishing Company DOI: 10.1142/S0218127417500912 A Memristive Hyperchaotic Multiscroll Jerk System with Controllable Scroll Numbers Chunhua Wang, Hu Xia∗ and Ling Zhou College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, P. R. China ∗[email protected] Received November 24, 2016; Revised March 26, 2017 A memristor is the fourth circuit element, which has wide applications in chaos generation. In this paper, a four-dimensional hyperchaotic jerk system based on a memristor is proposed, where the scroll number of the memristive jerk system is controllable. The new system is constructed by introducing one extra flux-controlled memristor into three-dimensional multiscroll jerk sys- tem. We can get different scroll attractors by varying the strength of memristor in this system without changing the circuit structure. Such a method for controlling the scroll number without changing the circuit structure is very important in designing the modern circuits and systems. The new memristive jerk system can exhibit a hyperchaotic attractor, which has more com- plex dynamic behavior. Furthermore, coexisting attractors are observed in the system. Phase portraits, dissipativity, equilibria, Lyapunov exponents and bifurcation diagrams are analyzed. Finally, the circuit implementation is carried out to verify the new system. Keywords: Hyperchaos; multiscroll attractor; memristor; circuit implementation. 1. Introduction they belong to common chaotic systems. On the In recent years, the generation of chaotic attrac- other hand, switch is used to control nonlinear func- tors has become a hot topic in the investigation of tion, which decides the number of saddle focal bal- ance index of 2, so as to adjust the scroll number Int. -
Generation of Multi-Scroll Attractors Without Equilibria Via Piecewise Linear Systems
Generation of Multi-Scroll Attractors Without Equilibria Via Piecewise Linear Systems R.J. Escalante-Gonz´alez,1, a) E. Campos-Cant´on,1, b) and Matthew Nicol2, c) 1)Divisi´onde Matem´aticas Aplicadas, Instituto Potosino de Investigaci´on Cient´ıfica y Tecnol´ogica A. C., Camino a la Presa San Jos´e2055, Col. Lomas 4 Secci´on,C.P. 78216, San Luis Potos´ı, S.L.P., M´exico. 2)Mathematics Department, University of Houston, Houston, Texas 77204-3008, USA. (Dated: 14 March 2017) In this paper we present a new class of dynamical system without equilibria which possesses a multi scroll attractor. It is a piecewise-linear (PWL) system which is simple, stable, displays chaotic behavior and serves as a model for analogous non- linear systems. We test for chaos using the 0-1 Test for Chaos of Ref.12. a)Electronic mail: [email protected] b)Electronic mail: [email protected] c)Electronic mail: [email protected] 1 Piecewise-linear (PWL) systems are switching systems composed of linear affine subsystems along with a rule which determines the acting subsystem. These systems are known to be capable of producing chaotic attractors, as in the well studied Chua's circuit. This paper discusses the generation of multiscroll attractors without equilibria based on PWL systems. I. INTRODUCTION In recent years the study of dynamical systems with complicated dynamics but with- out equilibria has attracted attention. Since the first dynamical system of this kind with a chaotic attractor was introduced in Ref.1 (Sprott case A), several works have investigated this topic.