Chaotic Systems

Author : Sundarapandian Vaidyanathan,Christos Volos
Publisher : Springer
Page : 600 pages
File Size : 54,9 Mb
Release : 2016-03-22
Category : Technology & Engineering
ISBN : 9783319302799

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Advances and Applications in Chaotic Systems by Sundarapandian Vaidyanathan,Christos Volos Pdf

This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.

Author : Thomas S. Parker,Leon Chua
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461234869

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Practical Numerical Algorithms for Chaotic Systems by Thomas S. Parker,Leon Chua Pdf

One of the basic tenets of science is that deterministic systems are completely predictable-given the initial condition and the equations describing a system, the behavior of the system can be predicted 1 for all time. The discovery of chaotic systems has eliminated this viewpoint. Simply put, a chaotic system is a deterministic system that exhibits random behavior. Though identified as a robust phenomenon only twenty years ago, chaos has almost certainly been encountered by scientists and engi neers many times during the last century only to be dismissed as physical noise. Chaos is such a wide-spread phenomenon that it has now been reported in virtually every scientific discipline: astronomy, biology, biophysics, chemistry, engineering, geology, mathematics, medicine, meteorology, plasmas, physics, and even the social sci ences. It is no coincidence that during the same two decades in which chaos has grown into an independent field of research, computers have permeated society. It is, in fact, the wide availability of inex pensive computing power that has spurred much of the research in chaotic dynamics. The reason is simple: the computer can calculate a solution of a nonlinear system. This is no small feat. Unlike lin ear systems, where closed-form solutions can be written in terms of the system's eigenvalues and eigenvectors, few nonlinear systems and virtually no chaotic systems possess closed-form solutions.

Author : Frank C. Hoppensteadt
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 46,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722758

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Analysis and Simulation of Chaotic Systems by Frank C. Hoppensteadt Pdf

Analysis and Simulation of Chaotic Systems is a text designed to be used at the graduate level in applied mathematics for students from mathematics, engineering, physics, chemistry and biology. The book can be used as a stand-alone text for a full year course or it can be heavily supplemented with material of more mathematical, more engineering or more scientific nature. Computations and computer simulations are used throughout this text to illustrate phenomena discussed and to supply readers with probes to use on new problems.

Author : Xiong Wang,Nikolay V. Kuznetsov,Guanrong Chen
Publisher : Springer Nature
Page : 661 pages
File Size : 55,6 Mb
Release : 2021-12-01
Category : Technology & Engineering
ISBN : 9783030758219

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Chaotic Systems with Multistability and Hidden Attractors by Xiong Wang,Nikolay V. Kuznetsov,Guanrong Chen Pdf

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 : Ivan Zelinka,Sergej Celikovský,Hendrik Richter,Guanrong Chen
Publisher : Springer
Page : 560 pages
File Size : 50,9 Mb
Release : 2010-03-10
Category : Technology & Engineering
ISBN : 9783642107078

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Evolutionary Algorithms and Chaotic Systems by Ivan Zelinka,Sergej Celikovský,Hendrik Richter,Guanrong Chen Pdf

This book discusses the mutual intersection of two fields of research: evolutionary computation, which can handle tasks such as control of various chaotic systems, and deterministic chaos, which is investigated as a behavioral part of evolutionary algorithms.

Author : Christian Beck,Friedrich Schögl
Publisher : Cambridge University Press
Page : 310 pages
File Size : 53,8 Mb
Release : 1993-07
Category : Mathematics
ISBN : 9780521433679

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Thermodynamics of Chaotic Systems by Christian Beck,Friedrich Schögl Pdf

This book deals with the various thermodynamic concepts used for the analysis of nonlinear dynamical systems. The most important invariants used to characterize chaotic systems are introduced in a way that stresses the interconnections with thermodynamics and statistical mechanics. Among the subjects treated are probabilistic aspects of chaotic dynamics, the symbolic dynamics technique, information measures, the maximum entropy principle, general thermodynamic relations, spin systems, fractals and multifractals, expansion rate and information loss, the topological pressure, transfer operator methods, repellers and escape. The more advanced chapters deal with the thermodynamic formalism for expanding maps, thermodynamic analysis of chaotic systems with several intensive parameters, and phase transitions in nonlinear dynamics.

Author : Robert Devaney
Publisher : CRC Press
Page : 251 pages
File Size : 53,9 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9780429981937

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An Introduction To Chaotic Dynamical Systems by Robert Devaney Pdf

The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry. Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 51,8 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9781475738964

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Chaotic Transport in Dynamical Systems by Stephen Wiggins Pdf

Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincaré Map. This serves as a starting point for the further motivation of the transport issues through the development of ideas in a non-perturbative framework with generalizations to higher dimensions as well as more general time dependence. A timely and important contribution to those concerned with the applications of mathematics.

Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Academic Press
Page : 433 pages
File Size : 51,7 Mb
Release : 2004
Category : Business & Economics
ISBN : 9780123497031

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Differential Equations, Dynamical Systems, and an Introduction to Chaos by Morris W. Hirsch,Stephen Smale,Robert L. Devaney Pdf

Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.

Author : Esteban Tlelo-Cuautle
Publisher : BoD – Books on Demand
Page : 326 pages
File Size : 47,5 Mb
Release : 2011-02-14
Category : Computers
ISBN : 9789533075648

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Chaotic Systems by Esteban Tlelo-Cuautle Pdf

This book presents a collection of major developments in chaos systems covering aspects on chaotic behavioral modeling and simulation, control and synchronization of chaos systems, and applications like secure communications. It is a good source to acquire recent knowledge and ideas for future research on chaos systems and to develop experiments applied to real life problems. That way, this book is very interesting for students, academia and industry since the collected chapters provide a rich cocktail while balancing theory and applications.

Author : Kehui Sun,Shaobo He,Huihai Wang
Publisher : Springer Nature
Page : 254 pages
File Size : 44,8 Mb
Release : 2022-09-04
Category : Science
ISBN : 9789811932731

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Solution and Characteristic Analysis of Fractional-Order Chaotic Systems by Kehui Sun,Shaobo He,Huihai Wang Pdf

This book highlights the solution algorithms and characteristic analysis methods of fractional-order chaotic systems. Fractal dimensions exist broadly in the study of nature and the development of science and technology. Fractional calculus has become a hot research area in nonlinear science. Fractional-order chaotic systems are an important part of fractional calculus. The book discusses the numerical solution algorithms and characteristic analysis of fractional-order chaotic systems and introduces the techniques to implement the systems with circuits. To facilitate a quick grasp, the authors present examples from their years of work in the appendix. Intended for graduate students and researchers interested in chaotic systems, the book helps one to build a theoretical and experimental foundation for the application of fractional-order chaotic systems.

Author : Charilaos Skiadas,Ioannis Dimotikalis
Publisher : World Scientific
Page : 435 pages
File Size : 42,5 Mb
Release : 2009
Category : Technology & Engineering
ISBN : 9789814271332

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Topics on Chaotic Systems by Charilaos Skiadas,Ioannis Dimotikalis Pdf

This volume includes the best papers presented at the CHAOS 2008 International Conference on Chaotic Modeling, Simulation and Applications. It provides a valuable collection of new ideas, methods, and techniques in the field of nonlinear dynamics, chaos, fractals and their applications in general science and in engineering sciences. It touches on many fields such as chaos, dynamical systems, nonlinear systems, fractals and chaotic attractors. It also covers mechanics, hydrofluid dynamics, chaos in meteorology and cosmology, Hamiltonian and quantum chaos, chaos in biology and genetics, chaotic control, and chaos in economy and markets, and chaotic simulations; thus, containing cutting-edge interdisciplinary research with high-interest applications. These contributions present new solutions by analyzing the relevant data and through the use of recent advances in different fields, especially in chaotic simulation methods and techniques.

Author : Ricardo Femat,Gualberto Solis-Perales
Publisher : Springer
Page : 202 pages
File Size : 48,8 Mb
Release : 2009-01-23
Category : Technology & Engineering
ISBN : 9783540693079

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Robust Synchronization of Chaotic Systems via Feedback by Ricardo Femat,Gualberto Solis-Perales Pdf

This pages include the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, our concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behavior and what synchronization phen- ena can be found under feedback interconnection. Our findings have caused surprise to us and have stimulated our astonishing capability. Perhaps, reader can imagine our faces with opens eyes like children seeing around objects; which are possibly obvious for others and novel for us. A compilation of our surprises about these findings is being described along this book. Book contains both objectives to share our ama- ment and to show our perspective on synchronization of chaotic systems. Thus, while we were writing the preface, we discussed its scope. Thinking as a book readers, we found that a preface should answer, in few words, the following question: What can the reader find in this book?, reader can find our steps toward understanding of c- otic behavior and the possibility of suppressing and synchronizing it. We firstly show the chaos suppression form experimental domain to potential implementation in high tech system as a levitation system based on High Temperature Superconductors (HTS). This chapter is used as departing point towards a more complicated problem the chaotic synchronization. Then, reader travels by the synchronization of the chaotic behavior world throughout distinct feedback approaches.

Author : Michelle M. Bright
Publisher : Unknown
Page : 16 pages
File Size : 49,9 Mb
Release : 1993
Category : Electronic
ISBN : NASA:31769000604457

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Desktop Chaotic Systems: Intuition and Visualization by Michelle M. Bright Pdf

Author : Zhong Li
Publisher : Springer
Page : 300 pages
File Size : 45,8 Mb
Release : 2006-08-02
Category : Computers
ISBN : 9783540332213

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Fuzzy Chaotic Systems by Zhong Li Pdf

This book presents the fundamental concepts of fuzzy logic and fuzzy control, chaos theory and chaos control. It also provides a definition of chaos on the metric space of fuzzy sets. The book raises many questions and generates a great potential to attract more attention to combine fuzzy systems with chaos theory. In this way it contains important seeds for future scientific research and engineering applications.