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Chua's Circuit: A Paradigm For Chaos

Chua's Circuit: A Paradigm For Chaos
Author: Rabinder N Madan
Publisher: World Scientific
Total Pages: 1089
Release: 1993-11-20
Genre:
ISBN: 9814504319
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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.

A Gallery of Chua Attractors

A Gallery of Chua Attractors
Author: Eleonora Bilotta
Publisher: World Scientific
Total Pages: 607
Release: 2008
Genre: Mathematics
ISBN: 9812790624
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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).

A Practical Guide for Studying Chua's Circuits

A Practical Guide for Studying Chua's Circuits
Author: Recai Kilic
Publisher: World Scientific
Total Pages: 219
Release: 2010
Genre: Computers
ISBN: 9814291145
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Autonomous and nonautonomous Chua''s circuits are of special significance in the study of chaotic system modeling, chaos-based science and engineering applications. Since hardware and software-based design and implementation approaches can be applied to Chua''s circuits, these circuits are also excellent educative models for studying and experimenting nonlinear dynamics and chaos. This book not only presents a collection of the author''s published papers on design, simulation and implementation of Chua''s circuits, it also provides a systematic approach to practising chaotic dynamics.

Chaos in Circuits and Systems

Chaos in Circuits and Systems
Author: Guanrong Chen
Publisher: World Scientific
Total Pages: 656
Release: 2002
Genre: Technology & Engineering
ISBN: 9810249330
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In this volume, leading experts present current achievements in the forefront of research in the challenging field of chaos in circuits and systems, with emphasis on engineering perspectives, methodologies, circuitry design techniques, and potential applications of chaos and bifurcation. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this field. It is suitable for readers ranging from graduate students, university professors, laboratory researchers and industrial practitioners to applied mathematicians and physicists in electrical, electronic, mechanical, physical, chemical and biomedical engineering and science.

Chaos in Nonlinear Oscillators

Chaos in Nonlinear Oscillators
Author: Muthusamy Lakshmanan
Publisher: World Scientific
Total Pages: 346
Release: 1996
Genre: Science
ISBN: 9789810221430
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This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.

Chaos in Electronics

Chaos in Electronics
Author: M.A. van Wyk
Publisher: Springer Science & Business Media
Total Pages: 489
Release: 2013-06-29
Genre: Technology & Engineering
ISBN: 9401589216
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Many dynamical systems in physics, chemistry and biology exhibit complex be haviour. The apparently random motion of a fluid is the best known example. How ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla tors is also included. End of proofs and examples are indicated by •. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: MVANWYK@TSAMAIL. TRSA. AC. ZA Email address of the first author: WHS@RAU3. RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.

Applications of Chaos and Nonlinear Dynamics in Engineering -

Applications of Chaos and Nonlinear Dynamics in Engineering -
Author: Santo Banerjee
Publisher: Springer Science & Business Media
Total Pages: 349
Release: 2011-09-10
Genre: Technology & Engineering
ISBN: 3642219217
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Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. This volume concentrates on reviewing the most relevant contemporary applications of chaotic nonlinear systems as they apply to the various cutting-edge branches of engineering. The book covers the theory as applied to robotics, electronic and communication engineering (for example chaos synchronization and cryptography) as well as to civil and mechanical engineering, where its use in damage monitoring and control is explored). Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications

Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume Iii. Chaos: Chua's Circuit And Complex Nonlinear Phenomena

Chua Lectures, The: From Memristors And Cellular Nonlinear Networks To The Edge Of Chaos - Volume Iii. Chaos: Chua's Circuit And Complex Nonlinear Phenomena
Author: Leon O Chua
Publisher: World Scientific
Total Pages: 244
Release: 2020-08-19
Genre: Technology & Engineering
ISBN: 981121591X
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This 4-volume compendium contains the verbatim hard copies of all color slides from the Chua Lecture Series presented at HP in Palo Alto, during the period from September 22 to November 24, 2015. Each lecture consists of 90 minutes, divided into a formal lecture, a discussion session, and an Encore of special trivia that the audience found mesmerizing.These lectures share some unique features of the classic Feynman Lectures on Physics, as much of the materials are presented in the unique style of the author, and the content is original as discovered or invented by the author himself. Unlike most technical books that suffer a notoriously short life span as their features could be superseded by superior models, this series of Chua lectures are intended to never be obsolete — many concepts and principles introduced are in fact new laws of nature, written in the language of sophomore-level mathematics, providing the foundation and the elan vital for initiating and nurturing future concepts and inventions.Volume III — presents an overview of the fascinating phenomenon called chaos, while immersing the audience with the sights and sound of chaos from the Chua Circuit, invented in 1984 by Leon Chua, and has now become the standard textbook example of chaos exhibited by a real nonlinear electronic circuit, and not by computer simulations.

Fractional-Order Nonlinear Systems

Fractional-Order Nonlinear Systems
Author: Ivo Petráš
Publisher: Springer Science & Business Media
Total Pages: 218
Release: 2011-05-30
Genre: Technology & Engineering
ISBN: 3642181015
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"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.

Chua's Circuit Implementations

Chua's Circuit Implementations
Author: Luigi Fortuna
Publisher: World Scientific
Total Pages: 222
Release: 2009
Genre: Technology & Engineering
ISBN: 9812839259
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Since the birth of the Chua circuit in 1983, a considerable number of fruitful, fascinating and relevant research topics have arisen. In honor of the 25th anniversary of the invention of Chua''s circuit, this book presents the 25 years of research on the implementation of Chua''s circuit, and also discusses future directions and emerging applications of recent results. The purpose of the book is to provide researchers, PhD students, and undergraduate students a research monograph containing both fundamentals on the topics and advanced results that have been recently obtained. With about 60 illustrations included in the book, it also shows the detailed schematics of several different implementations that can be easily reproduced with a low-cost experimental setup and PC-based measurement instrumentation.