A guide to the fascinating new concept of chaotic sychronization.

This book presents a comprehensive overview of the research and latest developments in the field of the dynamics of coupled and driven chaotic oscillators, aimed at a wide audience. Since 1990, there has been very active research devoted to the field, culminating in a considerable body of knowledge, while active research continues.The results presented in the book will be valuable for scientific analysis and explanation in various different scientific disciplines, with potential applications in medicine and engineering. The contents include a selection of the most basic theoretical results, as well as experiments and applications presented at a mathematical level suited to readers working in non-hard sciences. It will also be of interest to physicists and mathematicians looking for an introduction to the field./a

This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only basic knowledge of integer ordinary and fractional ordinary differential equations. Design applications are illustrated with the help of several physical models of practical interest.

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.

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.

Since the early 1990s, when synchronization of chaotic communication systems became a popular research subject, a vast number of scientific papers have been published. However, most of today’s books on chaotic communication systems deal exclusively with the systems where perfect synchronization is assumed, an assumption which separates theoretical from practical, real world, systems. This book is the first of its kind dealing exclusively with the synchronization techniques for chaotic communication systems. It describes a number of novel robust synchronization techniques, which there is a lack of, for single and multi-user chaotic communication systems published and highly cited in world’s leading journals in the area. In particular, it presents a solution to the problem of robust chaotic synchronization by presenting the first fully synchronized, highly secure, chaos based DS-CDMA system. The book fills a gap in the existing literature where a number of books exist that deal with chaos and chaotic communications but not with synchronization of chaotic communication systems. It also acts as a bridge between communication system theory and chaotic synchronization by carefully explaining the two concepts and demonstrating how they link into chaotic communication systems. The book also presents a detailed literature review on the topic of synchronization of chaotic communication systems. Furthermore, it presents the literature review on the general topic of chaotic synchronization and how those ideas led to the application of chaotic signals to secure chaotic communication systems. It therefore, in addition to presenting the state of the art systems, also presents a detailed history of chaotic communication systems. In summary, the book stands out in the field of synchronization techniques for chaotic communication systems.

Starting with an introduction to the fundamental physics in chaotic instabilities in laser systems, this comprehensive and unified reference goes on to present the techniques and technology of synchronization of chaos in coupled lasers, as well as the many applications to lasers and optics, communications, security and information technology. Throughout, it presents the current state of knowledge, including encoding/decoding techniques, performance of chaotic communication systems, random number generation, and novel communication technologies.

The book describes synchronization phenomena using both classical results and more recent developments.

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.

Controlling Chaos achieves three goals: the suppression, synchronisation and generation of chaos, each of which is the focus of a separate part of the book. The text deals with the well-known Lorenz, Rössler and Hénon attractors and the Chua circuit and with less celebrated novel systems. Modelling of chaos is accomplished using difference equations and ordinary and time-delayed differential equations. The methods directed at controlling chaos benefit from the influence of advanced nonlinear control theory: inverse optimal control is used for stabilization; exact linearization for synchronization; and impulsive control for chaotification. Notably, a fusion of chaos and fuzzy systems theories is employed. Time-delayed systems are also studied. The results presented are general for a broad class of chaotic systems. This monograph is self-contained with introductory material providing a review of the history of chaos control and the necessary mathematical preliminaries for working with dynamical systems.