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.
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.
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.
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.
This volume describes the use of simple analog circuits to study nonlinear dynamics, chaos and stochastic resonance. The circuit experiments that are described are mostly easy and inexpensive to reproduce, and yet these experiments come from the forefront of nonlinear dynamics research. The individual chapters describe why analog circuits are so useful for studying nonlinear dynamics, and include theoretical as well as experimental results from some of the leading researchers in the field. Most of the articles contain some tutorial sections for the less experienced readers.The audience for this book includes researchers in nonlinear dynamics, chaos and statistical physics as well as electrical engineering, and graduate and advanced undergraduate students in these fields.
Bifurcation and Chaos has dominated research in nonlinear dynamics for over two decades and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book is written to serve the above unfulfilled need.Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the qualitative study of high-dimensional nonlinear dynamical systems. Many of the qualitative methods and tools presented in this book were developed only recently and have not yet appeared in a textbook form.In keeping with the self-contained nature of this book, all topics are developed with an introductory background and complete mathematical rigor. Generously illustrated and written with a high level of exposition, this book will appeal to both beginners and advanced students of nonlinear dynamics interested in learning a rigorous mathematical foundation of this fascinating subject.
The basic procedures for designing and analysing electronic systems are based largely on the assumptions of linear behavior of the system. Nonlinearities inherent in all real applications very often cause unexpected and even strange behavior. This book presents an electronic engineer's perspective on chaos and complex behavior. It starts from basic mathematical notions which enable understanding of the observed phenomena, and guides the reader through the methodology and tools used in the laboratory and numerical experiments to interpretation and explanation of basic mechanisms. On typical circuit examples, it shows how the theoretical and empirical developments can be used in practice. Attention is drawn to applications of chaotic circuits as noise generators and the possible use of synchronized chaotic systems in information transmission and encryption. Chaos control is considered as a new, emerging area where electronic equipment and chaos theory could turn vital in biomedical and engineering issues.
The theory of transmission lines is a classical topic of electrical engineering. Recently this topic has received renewed attention and has been a focus of considerable research. This is because the transmisson line theory has found new and important applications in the area of high-speed VLSI interconnects, while it has retained its significance in the area of power transmission. In many applications, transmission lines are connected to nonlinear circuits. For instance, interconnects of high-speed VLSI chips can be modelled as transmission lines loaded with nonlinear elements. These nonlinearities may lead to many new effects such as instability, chaos, generation of higher order harmonics, etc. The mathematical models of transmission lines with nonlinear loads consist of the linear partial differential equations describing the current and voltage dynamics along the lines together with the nonlinear boundary conditions imposed by the nonlinear loads connected to the lines. These nonlinear boundary conditions make the mathematical treatment very difficult. For this reason, the analysis of transmission lines with nonlinear loads has not been addressed adequately in the existing literature. The unique and distinct feature of the proposed book is that it will present systematic, comprehensive, and in-depth analysis of transmission lines with nonlinear loads. - A unified approach for the analysis of networks composed of distributed and lumped circuits - A simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic form - Frequency and time domain multiport representations of any linear transmission line - A detailed analysis of the influence on the line characterization of the frequency and space dependence of the line parameters - A rigorous study of the properties of the analytical and numerical solutions of the network equations - The associated discrete circuits and the associated resisitive circuits of transmission lines - Periodic solutions, bifurcations and chaos in transmission lines connected to noninear lumped circuits
Wave or weak turbulence is a branch of science concerned with the evolution of random wave fields of all kinds and on all scales, from waves in galaxies to capillary waves on water surface, from waves in nonlinear optics to quantum fluids. In spite of the enormous diversity of wave fields in nature, there is a common conceptual and mathematical core which allows to describe the processes of random wave interactions within the same conceptual paradigm, and in the same language. The development of this core and its links with the applications is the essence of wave turbulence science (WT) which is an established integral part of nonlinear science.The book comprising seven reviews aims at discussing new challenges in WT and perspectives of its development. A special emphasis is made upon the links between the theory and experiment. Each of the reviews is devoted to a particular field of application (there is no overlap), or a novel approach or idea. The reviews cover a variety of applications of WT, including water waves, optical fibers, WT experiments on a metal plate and observations of astrophysical WT.
Chaos theory deals with the description of motion (in a general sense) which cannot be predicted in the long term although produced by deterministic system, as well exemplified by meteorological phenomena. It directly comes from the Lunar theory — a three-body problem — and the difficulty encountered by astronomers to accurately predict the long-term evolution of the Moon using “Newtonian” mechanics. Henri Poincaré's deep intuitions were at the origin of chaos theory. They also led the meteorologist Edward Lorenz to draw the first chaotic attractor ever published. But the main idea consists of plotting a curve representative of the system evolution rather than finding an analytical solution as commonly done in classical mechanics. Such a novel approach allows the description of population interactions and the solar activity as well. Using the original sources, the book draws on the history of the concepts underlying chaos theory from the 17th century to the last decade, and by various examples, show how general is this theory in a wide range of applications: meteorology, chemistry, populations, astrophysics, biomedicine, etc.
