Chaos and Time-Series Analysis

This book is the most comprehensive and clear text for learning dynamics and many related topics of fractals and complexity that I have encountered. I t is appropriate for both classroom use, and for scientists working in a wide variety of fields. The emphasis is on concepts and applications rather than proofs and derivations. I t is ' hands-on' , with practical exercises and a programming proj ect in each chapter. Dynamics programs, such as Berk eley Madonna (M acey, Oster, & Zahnley, 2000) or those by Sprott and Rowlands (1995) are most useful for additional explorations. There are three appendices. The first is a catalog of common chaotic systems, each with a graph, equations, typical parametric values and initial conditions, Lyapunov exponents, Kaplan-Yorke dimension, correlation dimension, and a maj or reference. The second appendix gives useful mathematical formulas. The third is a list of relevant j ournals. There are 715 bibliographic entries and 298 figures. There is an excellent support website with color versions of many of the figures and much supplementary and updated information (including answers to some of the exercises) at http: / / sprott.physics.wisc.edu/ chaostsa/. The I ntroduction (Chapter 1) mentions several examples of chaotic astronomical, physical, and nonphysical systems, many with photographs and diagrams. There is also a section on electrical circuits, which are of value whether one is intrinsically interested in electronic circuits or not. Some circuits can be easily and inexpensively constructed. A nice aspect of the book is the inclusion of brief footnotes on individuals. The programming proj ect concerns the logistic equation. The first exercise to derive a set of four first-order ordinary differential equations for the three-body problem is one on which many have spent much time since Poincaré first stumbled over it. I found myself trying to