IEEE CIRCUITS AND SYSTEMS MAGAZINE. FIRST QUARTER 2003 .... for Lur'e systems is also given, including master-slave syn- chronization, mutual ...
Book Reviews Ljupco Kocarev
Chaos in Circuits and Systems Edited by Guanrong Chen and Tetsushi Ueta World Scientific Publishing Co., Singapore (ISBN 981-02-4933-0) 2002
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haos in Circuits and Systems is an elucidating account of state-of-the-art nonlinear circuits and systems. Nonlinear phenomena and chaos are ubiquitous in nature and man-made systems. As a consequence, a large number of conference proceedings, research monographs, textbooks, and special journal issues have been published so far. Is there a need for yet another book on the same topic? Obviously the editors think there is. In their preface, the editors hope that “this book can serve as an updated and handy reference” for anybody working in the filed of nonlinear science. In the preface of the book Topics in Mathematical System Theory, the authors, R. E. Kalman, P. L. Falb and M. A. Arbib, wrote: “The child of three fathers and borne of circumstances, this book does not pretend to be a systematic treatise. Rather, it aims to present Mathematical System Theory as it is today – a lively, challenging, exciting, difficult, confused, rewarding, and largely unexplored field, one which is already very important and yet holds the promise of still bigger discoveries”. The same can be written for the book Chaos in Circuits and Systems: it is a child of many fathers aiming to present Nonlinear Circuits and Systems Theory as a lively and challenging field, which still holds the promise of new discoveries in both theory and application. The editors and the authors of this book did a great job in choosing and writing about different subjects, which are useful for almost everybody: university professors, graduate students, researchers and industrial practitioners. In brief, the book is a delight and, for the correct audience, it will be very successful. Chaos in Circuits and Systems, edited by Professors Chen and Ueta, is one of those essential books that should be found on the shelf of just about every nonlinear scientist. This special volume collects 29 chapters written by eminent scientists working in the field of nonlinear circuits and systems. Three articles on design methods for chaotic circuits open the book. The first article, “Chaotic Oscillators – Design Principles”, is an introduction to the design of chaotic oscillators from an electrical engineering point of view. In the second chapter, “Design Methodology for 22
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Autonomous Chaotic Oscillators”, the authors, A. S. Elwakil and M. P. Kennedy, propose design methodology for autonomous chaotic oscillators, based on the following four rules: 1) the nonlinearity in a chaotic oscillator should be introduced only by means of a passive device; 2) the nonlinear element should be separated from the linear building blocks such that the functionality of these blocks remains clear, ideal and independent of any parameters of the nonlinear element; 3) chaos should be reproducible with a model that does not depend on any device-specific parasitic effect; and 4) simple two-terminal nonlinear resistors should be used where possible. The basic advantage of adopting these design rules is that one can design a chaotic oscillator which is circuit and technology independent. The third article, “A Design Method for Chaotic Circuits Using Two Dimensional Oscillators”, introduces a system consisting of two oscillators coupled by diodes as a simple technique for chaos generation. In the chapter “Chaotic Wandering in Simple Coupled Chaotic Circuits”, the author, Y. Nishio, presents a circuit in which a nonlinear phenomenon called chaotic wandering may occur; and its statistical analysis is performed. The next two book chapters deal with phase-locked loops. In the first article entitled “Intermittent Chaos in PhaseLocked Loops”, T. Endo, A. Hasegawa and W. Ohno review various type of intermittent chaos, which may occur in phase-locked loop systems. It is interesting to note that a phase-locked loop (PLL) device, a popular integrated circuit module widely used in communication systems, may generate different varieties of chaos. In the sixth chapter, “Dynamical Chaos in Phase-Locked Loops”, the authors analyze chaos in PLLs and show that the phase-locked principle is a fruitful approach for chaos control. The article “A Chaotic Oscillator Based on Two-Port VCCS” introduces a four-dimensional chaotic oscillator based on two-port voltage-controlled current sources; the oscillator exhibits double-screw and quad-screw chaotic attractors. In the next chapter “A Generic Class of Chaotic and Hyper-Chaotic Circuits with Synchronization Methods”, the authors present an overview of chaotic and hyper-chaotic circuits, which can be represented in Lur’e form. A short overview about several synchronization methods developed for Lur’e systems is also given, including master-slave synchronization, mutual synchronization, robust synchronization, and impulsive synchronization. The next chapter, entitled “Some New Circuit Designs for chaos generation in simple three-dimensional autonomous systems. The tenth FIRST QUARTER 2003
chapter, “A Current Based VLSI Degree-Two Chaos Generator”, presents a chaos generator based upon two unstable oscillators with feedback to themselves. The chaotic nature of the signals is guaranteed by the Li-Yorke theorem through the generation of the period-three return map. In the next chapter, “Stochastic Analysis of Electrical Circuits”, the concept of Frobenius-Perron operators, used to study stochastic aspects of chaotic dynamical systems, is applied to investigate chaotic behavior of electrical circuits, such as switchedmode converters and sigma-delta modulators. The chapter “Chaotic Neuro-Computer” describes mixed analog/digital circuit implementation of a chaotic neurocomputer system. The authors suggest analog implementation of the neuron model (using a switched-capacitor integrated circuit technique) and digital implementation of the synaptic connections to accommodate a vast number of synapses. The system architecture with 10000 neurons and 100000000 synapses is illustrated. In the text chapter “Complex Dynamics Behavior in Nearly Symmetric Standard Cellular Neural Networks”, the authors M. Forti and A. Tesi investigate the robustness of complete stability with respect to small perturbations in a symmetric standard CNN, which is known to be completely stable: each trajectory converges to certain equilibrium point. They prove in a number of standard CNN configurations the existence of stable limit and more complicated attractors, arbitrarily close to the symmetry condition. The fourteenth chapter “Chaos in a PulseType Hardware Neuron Model” describes a pulse-type hardware neuron based on an asynchronous chaotic neuron model. The chapter “Bifurcations in Synaptically Coupled Bonhoffer-van der Pol Neurons” deals with the bifurcation of periodic solutions in model equations of two and tree Bonhoffer – van der Pol neurons coupled through characteristics of synaptic transmissions with a time delay. The chapter “Chaos in Power Electronics: an Overview” written by M. di Bernardo and C. K. Tse provides an overview of the chaotic dynamics and bifurcation scenarios observed in power electronics circuits. The chapter covers modeling approaches, analysis methods, and a classification of the common types of bifurcations observed in power electronics. The seventeenth chapter, “Use of Chaotic Switching for Harmonic Power Redistribution in Power Converters”, gives an evaluation of the chaotic carrier frequency modulation scheme on the spectral characteristics of switching converters. The next chapter entitled “Experimental Techniques for Investigating Chaos in Electronics” presents an overview of the commonly used laboratory techniques for studying nonlinear phenomena in electronic circuits. The nineteenth chapter “Nonlinear Dynamical Systems with Interrupted Characteristics: Bifurcation and Control” deals with a so-called Alpazur oscillator; the authors discuss bifurcation scenarios in this oscillator and suggest FIRST QUARTER 2003
control mechanisms for stabilizing periodic orbits. The next chapter, “Controller Synthesis for Periodically Forced Chaotic Systems”, considers the use of finite dimensional linear time-invariant controllers for stabilization of periodic solutions in a general class of nonlinear systems forced with sinus functions. In the article “Mechanism for Taming Chaos by Weak Harmonic Perturbation”, the author studies the mechanisms that lead to chaos suppression in a forced Rayleigh oscillator. Next, “Correlator-Based Chaotic Communication: Attainable Noise and Multipath Performance”, shows in a tutorial manner how the theory of conventional communication systems can be applied to chaotic modulation schemes. The authors give several examples of chaotic communication schemes with and without synchronization. In “Using Nonlinear Dynamics and Chaos to Solve Signal Processing Tasks”, the author M. J. Ogorzalek addresses a series of signal processing tasks, such as section-wise approximation, signal restoration, signal coding and compression. The twentyfourth chapter “Chaos Synchronization in a Noisy Environment Using Kalman Filters” deals with the problem of state space reconstruction given noisy signals from known chaotic systems. This problem is equivalent to chaos synchronization and is solved with the help of tools from optimal control theory, namely the Kalman filter. In the next chapter, “Identification of a Parameterized Family of Chaotic Dynamics from Time Series”, the authors consider the problem of identifying an unknown parameterized family of chaotic systems from a variety of its time series data with a change in the bifurcation parameters. “Cipher-Quasi-Chaotic Sequence with Application to Spreading Spectrum Communication Systems” discusses several applications of quasi-chaotic sequences in spread spectrum communication systems. The chapter “Image Processing in Tunneling Phase Logic Cellular Nonlinear Networks” presents simulations of operations in cellular nonlinear networks that could potentially be used to perform general computations in 2D arrays of simple locally connected nanoscale devices. In the next chapter, entitled “Numerical Approach to Bifurcation Analysis”, the authors investigate direct methods for evaluating the bifurcation parameter values of periodic solutions in nonlinear systems. The last chapter of this book, “Chaos in One-Dimensional Maps”, provides an introduction to chaos in one-dimensional maps. To summarize, the book under review is a valuable and timely addition to the current literature on chaos in circuits and systems. It provides the reader with a broad overview of recent progress in the lively and challenging field of nonlinear circuits and systems, and their applications in power electronics, communication, and computer sciences. This book is highly recommendable to anyone, a graduate student, a researcher or a professor, who studies nonlinear dynamics, circuits, devices, and systems. IEEE CIRCUITS AND SYSTEMS MAGAZINE
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