Perspectives of Nonlinear Dynamics

Volume 1
Erscheinungsjahr 2008
ISBN: 978-0-521-42632-9
Verlag: Cambridge University Press

Buch, Englisch, 520 Seiten, Format (B × H): 189 mm x 246 mm, Gewicht: 1155 g

The dynamics of physical, chemical, biological, or fluid systems generally must be described by non-linear 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 non-solitons; coupled maps and pattern dynamics; cellular automata.

Autoren/Hrsg.

Jackson, E. Atlee

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.