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Lozi H Non And Belykh Chaotic Attractors

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Lozi H Non And Belykh Chaotic Attractors

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Author : René Lozi
language : en
Publisher: CRC Press
Release Date : 2024-12-30

Lozi H Non And Belykh 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 2024-12-30 with Mathematics categories.

Over the past fifty years, the development of chaotic dynamical systems theory and its subsequent wide applicability in science and technology has been an extremely important achievement of modern mathematics. Chaotic attractors are not a fleeting curiosity, and their continued study is important for the progress of mathematics. This book collects several of the new relevant results on the most important of them: the Lozi, Hénon and Belykh attractors. Existence proofs for strange attractors in piecewise-smooth nonlinear Lozi-Hénon and Belykh maps are given. Generalization of Lozi map in higher dimensions, Markov partition or embedding into the 2D border collision normal form of this map are considered. K-symbol fractional order discrete-time and relationship between this map and maxtype difference equations are explored. Statistical self-similarity, control of chaotic transients, and target-oriented control of Hénon and Lozi attractors are presented. Controlling chimera and solitary states by additive noise in networks of chaotic maps, detecting invariant expanding cones for generating word sets to identify chaos in piecewise-linear maps, and studying border collision bifurcations in a piecewise linear duopoly model complete this book. This book is an essential companion for 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.

Robust Chaos And Its Applications

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Author : Elhadj Zeraoulia
language : en
Publisher: World Scientific
Release Date : 2012

Robust Chaos And Its Applications written by Elhadj Zeraoulia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.

Lozi Mappings

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Author : Zeraoulia Elhadj
language : en
Publisher: CRC Press
Release Date : 2013-08-17

Lozi Mappings written by Zeraoulia Elhadj and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-17 with Mathematics categories.

This book is a comprehensive collection of known results about the Lozi map, a piecewise-affine version of the Henon map. Henon map is one of the most studied examples in dynamical systems and it attracts a lot of attention from researchers, however it is difficult to analyze analytically. Simpler structure of the Lozi map makes it more suitable fo

Chua S Circuit A Paradigm For Chaos

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Author : Rabinder N Madan
language : en
Publisher: World Scientific
Release Date : 1993-11-20

Chua S Circuit A Paradigm For Chaos written by Rabinder N Madan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-11-20 with categories.

For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme simplicity and robustness has made it the circuit of choice for generating chaotic signals for practical applications.In addition to the 48 illuminating papers drawn from a recent two-part Special Issue (March and June, 1993) of the Journal of Circuits, Systems, and Computers devoted exclusively to Chua's circuit, several highly illustrative tutorials and incisive state-of-the-art reviews on the latest experimental, computational, and analytical investigations on chaos are also included. To enhance its pedagogical value, a diskette containing a user-friendly software and data base on many basic chaotic phenomena is attached to the book, as well as a gallery of stunningly colorful strange attractors.Beginning with an elementary (freshman-level physics) introduction on experimental chaos, the book presents a step-by-step guided tour, with papers of increasing complexity, which covers almost every conceivable aspects of bifurcation and chaos. The second half of the book contains many original materials contributed by world-renowned authorities on chaos, including L P Shil'nikov, A N Sharkovsky, M Misiurewicz, A I Mees, R Lozi, L O Chua and V S Afraimovich.The scope of topics covered is quite comprehensive, including at least one paper on each of the following topics: routes to chaos, 1-D maps, universality, self-similarity, 2-parameter renormalization group analysis, piecewise-linear dynamics, slow-fast dynamics, confinor analysis, symmetry breaking, strange attractors, basins of attraction, geometric invariants, time-series reconstruction, Lyapunov exponents, bispectral analysis, homoclinic bifurcation, stochastic resonance, synchronization, and control of chaos, as well as several novel applications of chaos, including secure communications, visual sensing, neural networks, dry turbulence, nonlinear waves and music.

Dynamical Systems Ergodic Theory And Applications

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Author : L.A. Bunimovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-04-05

Dynamical Systems Ergodic Theory And Applications written by L.A. Bunimovich 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 2000-04-05 with Mathematics categories.

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Dynamical Systems

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Author : René Lozi
language : en
Publisher: CRC Press
Release Date : 2025-06-23

Dynamical Systems 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 2025-06-23 with Mathematics categories.

This book offers a captivating exploration of the intersection between mathematics, chaos theory, and dynamical systems through the personal journeys of twelve renowned mathematicians and physicists from China, Europe, Russia, and the USA. The first section of the book provides an intimate look into the formative experiences and early steps of these scientists. In these life stories, the names of other famous mathematicians arise, crisscrossing all the stories in unexpected ways. The second part of the book explores the practical applications of chaotic attractors in various fields. These include chaos-based encryption in cryptography, sensor and actuator placement in Chua circuits for control systems, and chaotic dynamics in remote sensing for crop modeling. It also highlights the role of chaos theory in the development of memristors following Leon Chua’s 1971 discovery, leading to advances in nonlinear dynamics, hyperchaos, and memristor-based systems. The chapters further examine how chaos theory addresses modern challenges such as modeling COVID-19 spread using SEIR models and optimizing mobile network design, demonstrating the wide-reaching impact of chaotic systems in real-world applications. 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. This book includes a revised introduction and a new chapter. The remaining chapters were originally published in Journal of Difference Equations and Applications.

Progress In Nonlinear Science

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Author : Lev M. Lerman
language : en
Publisher:
Release Date : 2002

Progress In Nonlinear Science written by Lev M. Lerman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Nonlinear theories categories.

Bifurcations And Chaos In Piecewise Smooth Dynamical Systems

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Author : Zhanybai T. Zhusubaliyev
language : en
Publisher: World Scientific
Release Date : 2003

Bifurcations And Chaos In Piecewise Smooth Dynamical Systems written by Zhanybai T. Zhusubaliyev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick-slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general.

Chua S Circuit

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Author : Rabinder N. Madan
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1993

Chua S Circuit written by Rabinder N. Madan and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.

Nonlinear Dynamical Systems With Self Excited And Hidden Attractors

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Author : Viet-Thanh Pham
language : en
Publisher: Springer
Release Date : 2018-02-26

Nonlinear Dynamical Systems With Self Excited And Hidden Attractors written by Viet-Thanh Pham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-26 with Technology & Engineering categories.

This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with self-excited and hidden attractors. The book includes 20 chapters contributed by respected experts, which focus on various applications such as biological systems, memristor-based systems, fractional-order systems, finance systems, business cycles, oscillators, coupled systems, hyperchaotic systems, flexible robot manipulators, electronic circuits, and control models. Special attention is given to modeling, design, circuit realization, and practical applications to address recent research problems in nonlinear dynamical systems. The book provides a valuable reference guide to nonlinear dynamical systems for engineers, researchers, and graduate students, especially those whose work involves mechanics, electrical engineering, and control systems.

Lozi H Non And Belykh Chaotic Attractors

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