Chaotic Systems with Multistability and Hidden Attractors PDF Download

Author: Xiong Wang
Publisher: Springer Nature
ISBN: 3030758214
Category : Technology & Engineering
Languages : en
Pages : 661

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Book Description
This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scientific studies. This book is unique of its kind in the current literature, presenting broad scientific research topics including multistability and hidden attractors in unconventional chaotic systems, such as chaotic systems without equilibria, with only stable equilibria, with a curve or a surface of equilibria. The book describes many novel phenomena observed from chaotic systems, such as non-Shilnikov type chaos, coexistence of different types of attractors, and spontaneous symmetry breaking in chaotic systems. The book presents state-of-the-art scientific research progress in the field with both theoretical advances and potential applications. This book is suitable for all researchers and professionals in the areas of nonlinear dynamics and complex systems, including research professionals, physicists, applied mathematicians, computer scientists and, in particular, graduate students in related fields.

Author: Christoph Von Der Malsburg
Publisher: MIT Press
ISBN: 0262289040
Category : Medical
Languages : en
Pages : 367

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Book Description
An examination of how widely distributed and specialized activities of the brain are flexibly and effectively coordinated. A fundamental shift is occurring in neuroscience and related disciplines. In the past, researchers focused on functional specialization of the brain, discovering complex processing strategies based on convergence and divergence in slowly adapting anatomical architectures. Yet for the brain to cope with ever-changing and unpredictable circumstances, it needs strategies with richer interactive short-term dynamics. Recent research has revealed ways in which the brain effectively coordinates widely distributed and specialized activities to meet the needs of the moment. This book explores these findings, examining the functions, mechanisms, and manifestations of distributed dynamical coordination in the brain and mind across different species and levels of organization. The book identifies three basic functions of dynamic coordination: contextual disambiguation, dynamic grouping, and dynamic routing. It considers the role of dynamic coordination in temporally structured activity and explores these issues at different levels, from synaptic and local circuit mechanisms to macroscopic system dynamics, emphasizing their importance for cognition, behavior, and psychopathology. Contributors Evan Balaban, György Buzsáki, Nicola S. Clayton, Maurizio Corbetta, Robert Desimone, Kamran Diba, Shimon Edelman, Andreas K. Engel, Yves Fregnac, Pascal Fries, Karl Friston, Ann Graybiel, Sten Grillner, Uri Grodzinski, John-Dylan Haynes, Laurent Itti, Erich D. Jarvis, Jon H. Kaas, J.A. Scott Kelso, Peter König, Nancy J. Kopell, Ilona Kovács, Andreas Kreiter, Anders Lansner, Gilles Laurent, Jörg Lücke, Mikael Lundqvist, Angus MacDonald, Kevan Martin, Mayank Mehta, Lucia Melloni, Earl K. Miller, Bita Moghaddam, Hannah Monyer, Edvard I. Moser, May-Britt Moser, Danko Nikolic, William A. Phillips, Gordon Pipa, Constantin Rothkopf, Terrence J. Sejnowski, Steven M. Silverstein, Wolf Singer, Catherine Tallon-Baudry, Roger D. Traub, Jochen Triesch, Peter Uhlhaas, Christoph von der Malsburg, Thomas Weisswange, Miles Whittington, Matthew Wilson

Author: Christopher K.R.T. Jones
Publisher: Springer Science & Business Media
ISBN: 1461301173
Category : Mathematics
Languages : en
Pages : 278

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Book Description
Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.

Author: Mario Bernardo
Publisher: Springer Science & Business Media
ISBN: 1846287081
Category : Mathematics
Languages : en
Pages : 497

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Book Description
This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.

Author: Jean-Marc Gambaudo
Publisher: World Scientific
ISBN: 9789810242176
Category : Science
Languages : en
Pages : 328

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Book Description
This book focuses on the interactions between discrete and geometric dynamical systems, and between dynamical systems and theoretical physics and computer science. Accordingly, the contributions revolve around two main topics: (1) interaction between geometric and symbolic systems, with emphasis on tiling problems for quasicrystals, substitutions and their multidimensional generalizations, geodesic and horocycle flow, adic systems; (2) dynamical systems: geometry and chaos, with special interest in smooth ergodic theory, statistical and multifractal properties of chaotic systems, stability and turbulence in extended complex systems.

Author: J. A. Scott Kelso
Publisher: MIT Press
ISBN: 9780262611312
Category : Medical
Languages : en
Pages : 368

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Book Description
foreword by Hermann Haken For the past twenty years Scott Kelso's research has focused on extending the physical concepts of self- organization and the mathematical tools of nonlinear dynamics to understand how human beings (and human brains) perceive, intend, learn, control, and coordinate complex behaviors. In this book Kelso proposes a new, general framework within which to connect brain, mind, and behavior.Kelso's prescription for mental life breaks dramatically with the classical computational approach that is still the operative framework for many newer psychological and neurophysiological studies. His core thesis is that the creation and evolution of patterned behavior at all levels--from neurons to mind--is governed by the generic processes of self-organization. Both human brain and behavior are shown to exhibit features of pattern-forming dynamical systems, including multistability, abrupt phase transitions, crises, and intermittency. Dynamic Patterns brings together different aspects of this approach to the study of human behavior, using simple experimental examples and illustrations to convey essential concepts, strategies, and methods, with a minimum of mathematics. Kelso begins with a general account of dynamic pattern formation. He then takes up behavior, focusing initially on identifying pattern-forming instabilities in human sensorimotor coordination. Moving back and forth between theory and experiment, he establishes the notion that the same pattern-forming mechanisms apply regardless of the component parts involved (parts of the body, parts of the nervous system, parts of society) and the medium through which the parts are coupled. Finally, employing the latest techniques to observe spatiotemporal patterns of brain activity, Kelso shows that the human brain is fundamentally a pattern forming dynamical system, poised on the brink of instability. Self-organization thus underlies the cooperative action of neurons that produces human behavior in all its forms.

Author: Sundarapandian Vaidyanathan
Publisher: Academic Press
ISBN: 0128175834
Category : Technology & Engineering
Languages : en
Pages : 542

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Book Description
Backstepping Control of Nonlinear Dynamical Systems addresses both the fundamentals of backstepping control and advances in the field. The latest techniques explored include 'active backstepping control', 'adaptive backstepping control', 'fuzzy backstepping control' and 'adaptive fuzzy backstepping control'. The reference book provides numerous simulations using MATLAB and circuit design. These illustrate the main results of theory and applications of backstepping control of nonlinear control systems. Backstepping control encompasses varied aspects of mechanical engineering and has many different applications within the field. For example, the book covers aspects related to robot manipulators, aircraft flight control systems, power systems, mechanical systems, biological systems and chaotic systems. This multifaceted view of subject areas means that this useful reference resource will be ideal for a large cross section of the mechanical engineering community. - Details the real-world applications of backstepping control - Gives an up-to-date insight into the theory, uses and application of backstepping control - Bridges the gaps for different fields of engineering, including mechanical engineering, aeronautical engineering, electrical engineering, communications engineering, robotics and biomedical instrumentation

Author: Raina Robeva
Publisher: Academic Press
ISBN: 0128140690
Category : Mathematics
Languages : en
Pages : 436

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Book Description
Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences. - Integrates a comprehensive selection of tools from computational biology into educational or research programs - Emphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulations - Contains scalable material for use in undergraduate and graduate-level classes and research projects - Introduces the reader to freely-available professional software - Supported by illustrative datasets and adaptable computer code

Author: Bernd Blasius
Publisher: World Scientific
ISBN: 9812771581
Category : Mathematics
Languages : en
Pages : 257

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Book Description
This collection of review articles is devoted to the modeling of ecological, epidemiological and evolutionary systems. Theoretical mathematical models are perhaps one of the most powerful approaches available for increasing our understanding of the complex population dynamics in these natural systems. Exciting new techniques are currently being developed to meet this challenge, such as generalized or structural modeling, adaptive dynamics or multiplicative processes. Many of these new techniques stem from the field of nonlinear dynamics and chaos theory, where even the simplest mathematical rule can generate a rich variety of dynamical behaviors that bear a strong analogy to biological populations.

Author: Jan Awrejcewicz
Publisher: World Scientific
ISBN: 981122191X
Category : Science
Languages : en
Pages : 561

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Book Description
In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.