Chaotic Behaviour of Deterministic Dissipative Systems

This is a graduate text surveying both the theoretical and experimental aspects of chaotic behaviour. Over the course of the past two decades it has been discovered that relatively simple, deterministic, nonlinear mathematical models that describe dynamic phenomena in various physical, chemical, biological and other systems yield solutions which are aperiodic and depend very sensitively on the initial conditions. This phenomenon is known as deterministic chaos. The authors present chaos as a model of many seemingly random processes in nature. Basic notions from the theory of dynamical systems and bifurcation theory, together with the properties of chaotic solutions, are then described and are illustrated by examples. A review of the numerical methods used both in studies of mathematical models and in the interpretation of experimental data is also provided.

"Among the rapidly growing number of books exhibiting different aspects of dynamically induced chaotic behavior, the book under review takes its own place for two reasons: First, it is mainly oriented toward applications. Second, it reflects a view and a set of results on this subject that were developed by the Prague research group studying dynamical systems and their applications." Alexander I. Khibnik, Quarterly Review of Biology, "...should be of use to experimentalists--as a comprehensive survey of the field up to around 1989." James D. Meiss, Mathematical Reviews, "...an excellent compendium of numerous contributions to the field of chaos science...the book reveals the continuing struggke to describe the physical universe in mathematical terms." Biophysical Journal, "This is a very well-written text of special interest to anyone interested in, or trying to model, non-periodic or chaotic behavior. Although this book is written in textbook format, it could serve either as a textbook or a very useful reference....Chaotic Behavior of Deterministic Dissipative Systems should be of interst to physicists, mathematicians, engineers, and biologists. Since it can serve as either a textbook or a useful reference, it should be made available to both individual and reference libraries." Applied Machanics Review (American Society of Mechanical Engineers), "The book Chaotic Behaviour of Deterministic Dissipative Systems, is an excellent compendium of numerous contributions to the field of chaos science, mostly from the 1980's." Charles L. Webber, Jr., Biophysical Journal