The Genesis Of Chuas Circuit

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.

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.

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.

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.

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).

This invaluable book is a unique collection of tributes to outstanding discoveries pioneered by Leon Chua in nonlinear circuits, cellular neural networks, and chaos. It is comprised of three parts. The first OCo cellular nonlinear networks, nonlinear circuits and cellular automata OCo deals with Chua''s Lagrangian circuits, cellular wave computers, bio-inspired robotics and neuro-morphic architectures, toroidal chaos, synaptic cellular automata, history of Chua''s circuits, cardiac arrhythmias, local activity principle, symmetry breaking and complexity, bifurcation trees, and Chua''s views on nonlinear dynamics of cellular automata. Dynamical systems and chaos is the scope of the second part of the book, where we find genius accounts on theory and application of Julia set, stability of dynamical networks, chaotic neural networks and neocortical dynamics, dynamics of piecewise linear systems, chaotic mathematical circuitry, synchronization of oscillators, models of catastrophic events, control of chaotic systems, symbolic dynamics, and solitons. First hand accounts on the discovery of memristors in HP Labs, historical excursions into OCyancient memristorsOCO, analytical analysis of memristors, and hardware memristor emulators are presented in the third and final part of the book.The book is quintessence of ideas on future and emergent hardware, analytic theories of complex dynamical systems and interdisciplinary physics. It is a true Renaissance volume where bright ideas of electronics, mathematics and physics enlighten facets of modern science.The unique DVD covers the artistic aspects of chaos, such as several stunningly melodious musical compositions using chaotic atttractors, a virtual gallery of hundreds of colorful attractors, and even a cartoon-like play on the genesis of Chua''s circuit that was based on a widely acclaimed performance in Rome and other venues in Italy. In short, it is a veritable kaleiscope of never-before-published historical, pedagogical, and futuristic technical visions on three timely topics of intense interest for both lay readers and experts alike."

In this book, leading researchers present their current work in the challenging area of chaos control in nonlinear circuits and systems, with emphasis on practical methodologies, system design techniques and applications. A combination of overview, tutorial and technical articles, the book describes state-of-the-art research on significant problems in this area. The scope and aim of this book are to bridge the gap between chaos control methods and circuits and systems. It is an ideal starting point for anyone who needs a fundamental understanding of controlling chaos in nonlinear circuits and systems.

The book is a compilation of selected papers from the conference on Physics and Control 2009, presenting a unified perspective underlying the thematics and strategies related to the control of physical systems with emerging applications in physics, engineering, chemistry, biology and other natural sciences. The selected papers reflect the state-of-the-art of the more advanced theoretical and practical studies in the field of control of complex systems. The contributions provide a comprehensive view on some selected topics of particular importance at the disciplinary borderline between Physics and Control.

Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MATLAB®. The book first covers the necessary mathematical preliminaries, including testing of stability. It then describes the modeling of systems from natural science, focusing on one- and two-dimensional continuous and discrete time models. Moving on to chaotic dynamics, the authors discuss ways to study chaos, types of chaos, and methods for detecting chaos. They also explore chaotic dynamics in single and multiple species systems. The text concludes with a brief discussion on models of mechanical systems and electronic circuits. Suitable for advanced undergraduate and graduate students, this book provides a practical understanding of how the models are used in current natural science and engineering applications. Along with a variety of exercises and solved examples, the text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.