Perspectives of Nonlinear Dynamics: Volume 1 by E. Atlee Jackson (English) Paper

Publisher Description

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincare maps and map-dynamics; empirical computational sciences vis-a-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.

Author Biography

E. ATLEE JACKSON is Professor of Physics, Emeritus, former Director of the Center for Complex System's Research at the University of Illinois at Urbana-Champaign, and a Fellow of the American Physical Society. He has taught and performed research on nonlinear dynamic phenomena for forty years, and is the author of the two-volume Perspectives of Nonlinear Dynamics.

Table of Contents

Preface; Acknowledgements; Concepts related to nonlinear dynamics: historical outline; 1. In the beginning ...; 2. A potpourri of basic concepts; 3. First order differential systems (n = 1); 4. Models based on first order difference equations; 5. Second order differential systems (n = 2); Appendices; Bibliography; References by topics; Index.

Promotional "Headline"

In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts.

Description for Bookstore

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts.

Description for Library

The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts.

Details