This book is a monograph on chaos in dissipative systems written for those working in the physical sciences. Emphasis is on symbolic description of the dynamics and various characteristics of the attractors, and written from the view-point of practical applications without going into formal mathematical rigour. The author used elementary mathematics and calculus, and relied on physical intuition whenever possible. Substantial attention is paid to numerical techniques in the study of chaos. Part of the book is based on the publications of Chinese researchers, including those of the author's collaborators.

Latest Edition: Applied Symbolic Dynamics and Chaos (2nd Edition)Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.

Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor. Contents: Preface to the Second Edition Preface to the First Edition Introduction Symbolic Dynamics of Unimodal Maps Maps with Multiple Critical Points Symbolic Dynamics of Circle Maps Symbolic Dynamics of Two-Dimensional Maps Application to Ordinary Differential Equations Counting the Number of Periodic Orbits Symbolic Dynamics and Grammatical Complexity Symbolic Dynamics and Knot Theory Appendix References Index Readership: Researchers and students interested in chaotic dynamics. Keywords: Symbolic Dynamics;ChaosReview: Key Features: No previous knowledge of dynamical systems theory is required in order to read this book The revisions concern mainly the application to ordinary differential equations via constructing two-dimensional symbolic dynamics of the corresponding Poincare maps

The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design DC-DC converters are typical switching systems which have plenty of nonlinear behaviors, such as bifurcation and chaos. The nonlinear behaviors of DC-DC converters have been studied heavily over the past 20 years, yet researchers are still unsure of the practical application of bifurcations and chaos in switching converters. The electromagnetic interference (EMI), which resulted from the high rates of changes of voltage and current, has become a major design criterion in DC-DC converters due to wide applications of various electronic devices in industry and daily life, and the question of how to reduce the annoying, harmful EMI has attracted much research interest. This book focuses on the analysis and application of chaos to reduce harmful EMI of DC-DC converters. After a review of the fundamentals of chaos behaviors of DC-DC converters, the authors present some recent findings such as Symbolic Entropy, Complexity and Chaos Point Process, to analyze the characters of chaotic DC-DC converters. Using these methods, the statistic characters of chaotic DC-DC converters are extracted and the foundations for the following researches of chaotic EMI suppression are reinforced. The focus then transfers to estimating the power spectral density of chaotic PWM converters behind an introduction of basic principles of spectrum analysis and chaotic PWM technique. Invariant Density, and Prony and Wavelet analysis methods are suggested for estimating the power spectral density of chaotic PWM converters. Finally, some design-oriented applications provide a good example of applying chaos theory in engineering practice, and illustrate the effectiveness on suppressing EMI of the proposed chaotic PWM. Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design Approaches the subject in a systematic manner from analyzing method, chaotic phenomenon and EMI characteristics, analytical methods for chaos, and applying chaos to reduce EMI (electromagnetic interference) Highlights advanced research work in the fields of statistic characters of nonlinear behaviors and chaotic PWM technology to suppress EMI of switching converters Bridges the gap between numerical theory and real-world applications, enabling power electronics designers to both analyze the effects of chaos and leverage these effects to reduce EMI

Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.