The Theory Of Chaotic Attractors
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The Theory Of Chaotic Attractors
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Author : Brian R. Hunt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-05
The Theory Of Chaotic Attractors written by Brian R. Hunt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.
The editors felt that the time was right for a book on an important topic, the history and development of the notions of chaotic attractors and their "natu ral" invariant measures. We wanted to bring together a coherent collection of readable, interesting, outstanding papers for detailed study and comparison. We hope that this book will allow serious graduate students to hold seminars to study how the research in this field developed. Limitation of space forced us painfully to exclude many excellent, relevant papers, and the resulting choice reflects the interests of the editors. Since James Alan Yorke was born August 3, 1941, we chose to have this book commemorate his sixtieth birthday, honoring his research in this field. The editors are four of his collaborators. We would particularly like to thank Achi Dosanjh (senior editor math ematics), Elizabeth Young (assistant editor mathematics), Joel Ariaratnam (mathematics editorial), and Yong-Soon Hwang (book production editor) from Springer Verlag in New York for their efforts in publishing this book.
Chaotic Evolution And Strange Attractors
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Author : David Ruelle
language : en
Publisher: Cambridge University Press
Release Date : 1989-09-07
Chaotic Evolution And Strange Attractors written by David Ruelle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-09-07 with Mathematics categories.
This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.
Hyperbolic Chaos
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Author : Sergey P. Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-20
Hyperbolic Chaos written by Sergey P. Kuznetsov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-20 with Science categories.
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Turbulence Strange Attractors And Chaos
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Author : David Ruelle
language : en
Publisher: World Scientific
Release Date : 1995
Turbulence Strange Attractors And Chaos written by David Ruelle and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
The present collection of reprints covers the main contributions of David Ruelle, and coauthors, to the theory of chaos and its applications. Several of the papers reproduced here are classics in the field. Others (that were published in less accessible places) may still surprise the reader.The collection contains mathematical articles relevant to chaos, specific articles on the theory, and articles on applications to hydrodynamical turbulence, chemical oscillations, etc.A sound judgement of the value of techniques and applications is crucial in the interdisciplinary field of chaos. For a critical assessment of what has been achieved in this area, the present volume is an invaluable contribution.
Handbook Of Applications Of Chaos Theory
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Author : Christos H. Skiadas
language : en
Publisher: CRC Press
Release Date : 2017-12-19
Handbook Of Applications Of Chaos Theory written by Christos H. Skiadas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.
A Gallery Of Chua Attractors
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Author : Eleonora Bilotta
language : en
Publisher: World Scientific
Release Date : 2008
A Gallery Of Chua Attractors written by Eleonora Bilotta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Chaos is considered as one of the most important concepts in modern science. It originally appeared only in computer simulation (the famous Lorenz equation of 1963), but this changed with the introduction of Chua's oscillator (1986) — a simple electronic circuit with the ability to generate a vast range of chaotic behaviors. With Chua's circuit, chaos became a physical phenomenon, readily understood and represented in mathematical language. Yet, even so, it is still difficult for the non-specialist to appreciate the full variety of behaviors that the system can produce.This book aims to bridge the gap. A gallery of nearly 900 “chaotic attractors” — some generated by Chua's physical circuit, the majority through computer simulation of the circuit and its generalizations — are illustrated as 3D color images, time series and fast Fourier transform algorithms. For interested researchers, also presented is the information necessary to replicate the behaviors and images. Finally, how the fractal richness can be plied to artistic ends in generating music and interesting sounds is shown; some examples are included in the DVD-ROM which comes with the book.The contents have also appeared in the International Journal of Bifurcation and Chaos (2007).
Recent Improvements In The Theory Of Chaotic Attractors
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Author : René Lozi
language : en
Publisher: CRC Press
Release Date : 2025-02-19
Recent Improvements In The Theory Of Chaotic Attractors written by René Lozi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-19 with Mathematics categories.
This book presents some exceptional developments in chaotic attractor theory encompassing several new directions of research such as three-dimensional axiom A-diffeomorphisms, Shilnikov attractors, dendrites and finite graphs. The theory of chaotic attractors has experienced exceptional development over the last fifty years since the revelation of chaos in mathematics (invented by James Yorke) and symbolized by the “butterfly effect”. Relevant new results have been collected in this book, including: Some remarks on minimal sets on dendrites and finite graphs and the study of recurrence and nonwandering sets of local dendrite maps. Ramified continua as global attractors of C1- smooth self-maps of a cylinder close to skew products Chaotic behaviour of countable products of homeomorphism groups and dynamics of three-dimensional axiom A-diffeomorphisms with two-dimensional attractors and repellers. The search for invariant sets of the generalized tent map and quasi-hyperbolic regime in a certain family of 2-D piecewise linear map. Shilnikov attractors of three-dimensional flows and maps, right fractional calculus to inverse-time chaotic maps and asymptotic stability analysis and diffeomorphisms with infinitely many Smale horseshoes. The theory of chaotic attractor is also used as a core for evolutionary algorithms and metaheuristic optimizers in this volume. This book will be of great value to students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications. The chapters in this book were originally published in Journal of Difference Equations and Applications.
An Exploration Of Dynamical Systems And Chaos
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Author : John H. Argyris
language : en
Publisher: Springer
Release Date : 2015-04-24
An Exploration Of Dynamical Systems And Chaos written by John H. Argyris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Technology & Engineering categories.
This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany
Strange Nonchaotic Attractors
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Author : Ulrike Feudel
language : en
Publisher: World Scientific
Release Date : 2006
Strange Nonchaotic Attractors written by Ulrike Feudel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Business & Economics categories.
This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed. Key Features Topics are suitable for various disciplines dealing with nonlinear dynamics (mechanics, physics, nonlinear optics, hydrodynamics, chemical kinetics, etc.) A variety of theoretical tools is supplied to reveal different characteristics of strange nonchaotic behavior Readership: Graduate students and researchers in nonlinear science.
Nonlinear Dynamics And Chaos
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Author : J. M. T. Thompson
language : en
Publisher: John Wiley & Sons
Release Date : 2002-02-15
Nonlinear Dynamics And Chaos written by J. M. T. Thompson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-15 with Science categories.
Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos. Expands on the bestselling, highly regarded first edition A new chapter which will cover the new research in the area since first edition Glossary of terms and a bibliography have been added All figures and illustrations will be 'modernised' Comprehensive and systematic account of nonlinear dynamics and chaos, still a fast-growing area of applied mathematics Highly illustrated Excellent introductory text, can be used for an advanced undergraduate/graduate course text