Perspectives of Nonlinear Dynamics: Volume 1

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

E. Atlee Jackson (Author)

9780521426329, Cambridge University Press

Paperback, published 31 January 1992

520 pages
24.6 x 18.9 x 2.7 cm, 0.92 kg

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; Poincaré maps and map-dynamics; empirical computational sciences vis-á-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.

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.

Subject Areas: Applied mathematics [PBW], Mathematics [PB]