This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Author(s): Christian Kuehn (auth.)
Series: Applied Mathematical Sciences 191
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 814
Tags: Dynamical Systems and Ergodic Theory; Theoretical, Mathematical and Computational Physics; Computational Mathematics and Numerical Analysis; Ordinary Differential Equations; Probability Theory and Stochastic Processes
Front Matter....Pages i-xiii
Introduction....Pages 1-17
General Fenichel Theory....Pages 19-51
Geometric Singular Perturbation Theory....Pages 53-70
Normal Forms....Pages 71-89
Direct Asymptotic Methods....Pages 91-112
Tracking Invariant Manifolds....Pages 113-157
The Blowup Method....Pages 159-196
Singularities and Canards....Pages 197-237
Advanced Asymptotic Methods....Pages 239-293
Numerical Methods....Pages 295-325
Computing Manifolds....Pages 327-357
Scaling and Delay....Pages 359-396
Oscillations....Pages 397-430
Chaos in Fast-Slow Systems....Pages 431-475
Stochastic Systems....Pages 477-524
Topological Methods....Pages 525-551
Spatial Dynamics....Pages 553-582
Infinite Dimensions....Pages 583-617
Other Topics....Pages 619-663
Applications....Pages 665-704
Back Matter....Pages 705-814
