Synopses & Reviews
The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.
Review
"The advantages of the book are the clarity of the writing and the unique and effective way in which the basic concepts are introduced." Sergei A. Dovbysh, Mathematical Reviews
Synopsis
New edition of a very successful undergraduate text on chaos.
Synopsis
Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. A special feature is the inclusion of both analytic and computer exercises with which the reader may expand upon the many numerical simulations included in the book. This allows learning through participation, without the extensive scientific background demanded by more advanced books. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. Experimental data from a chaotic pendulum are analyzed using methods of nonlinear time series analysis. With the help of new computer programs provided in the book (and also available from one of the authors on an optional diskette), readers and students can learn about these methods and use them to characterize their own data. The second edition also explains methods for short-term prediction and control. Spatio-temporal chaos is now introduced with examples from fluid dynamics, crystal growth, and other areas. The number of references has more than doubled; solutions are included to selected exercises. This new edition of Chaotic dynamics can be used as a text for a unit on chaos for physics and engineering students at the second- and third-year level. Such a unit would fit very well into modern physics and classical mechanics courses.
Synopsis
The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.
Table of Contents
1. Introduction; 2. Some helpful tools; 3. Visualization of the pendulum's dynamics; 4. Toward an understanding of chaos; 5. The characterization of chaotic attractors; 6. Experimental characterization, prediction, and modification of chaotic states; 7. Chaos broadly applied; Further reading; Appendix A. Numerical integration - Runge-Kutta method; Appendix B. Computer program listings; References; Index.