Perspectives of nonlinear dynamics

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Bibliographic Information

Perspectives of nonlinear dynamics

E. Atlee Jackson

Cambridge University Press, 1989-1990

  • v. 1
  • v. 2

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Note

Bibliography: v. 1: p. [421]-452. v. 2: p. [553]-584

Includes index

Description and Table of Contents

Volume

v. 1 ISBN 9780521345040

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.

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.
Volume

v. 2 ISBN 9780521354585

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 and its companion volume, Perspectives of nonlinear dynamics, volume 1, the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations. The text is complemented by copious references, extensive historical and bibliographical notes, exercises and examples, and appendices giving more details of some mathematical ideas. Each chapter includes an extensive section commentary on the exercises and their solution. Graduate students and research workers in physics, applied mathematics, chemistry, biology and engineering will welcome these volumes as the first broad introduction to this important major field of research.

Table of Contents

  • Preface
  • Acknowledgements
  • 6. Models based on second order difference equations
  • 7. Models based on third order differential systems
  • 8. 'Moderate-order' systems
  • 9. Solitaires: solitons and nonsolitons
  • 10. Coupled maps (CM) and cellular automata (CA)
  • Epilogue
  • Appendices
  • Bibliography
  • References
  • Cumulative Index (Volumes 1 and 2).

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