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  • Textbook
  • © 2015

Multiple Time Scale Dynamics

Authors:

  • Interdisciplinary approach to multiple time scale dynamics

  • Includes many exercises and direct transition to research-level questions

  • Links different mathematical areas and different viewpoints

  • Highly illustrated

Part of the book series: Applied Mathematical Sciences (AMS, volume 191)

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  • ISBN: 978-3-319-12316-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
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  • Tax calculation will be finalised during checkout
Softcover Book USD 39.99 USD 79.99
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Hardcover Book USD 59.99 USD 119.99
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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xiii
  2. Introduction

    • Christian Kuehn
    Pages 1-17
  3. General Fenichel Theory

    • Christian Kuehn
    Pages 19-51
  4. Geometric Singular Perturbation Theory

    • Christian Kuehn
    Pages 53-70
  5. Normal Forms

    • Christian Kuehn
    Pages 71-89
  6. Direct Asymptotic Methods

    • Christian Kuehn
    Pages 91-112
  7. Tracking Invariant Manifolds

    • Christian Kuehn
    Pages 113-157
  8. The Blowup Method

    • Christian Kuehn
    Pages 159-196
  9. Singularities and Canards

    • Christian Kuehn
    Pages 197-237
  10. Advanced Asymptotic Methods

    • Christian Kuehn
    Pages 239-293
  11. Numerical Methods

    • Christian Kuehn
    Pages 295-325
  12. Computing Manifolds

    • Christian Kuehn
    Pages 327-357
  13. Scaling and Delay

    • Christian Kuehn
    Pages 359-396
  14. Oscillations

    • Christian Kuehn
    Pages 397-430
  15. Chaos in Fast-Slow Systems

    • Christian Kuehn
    Pages 431-475
  16. Stochastic Systems

    • Christian Kuehn
    Pages 477-524
  17. Topological Methods

    • Christian Kuehn
    Pages 525-551
  18. Spatial Dynamics

    • Christian Kuehn
    Pages 553-582
  19. Infinite Dimensions

    • Christian Kuehn
    Pages 583-617
  20. Other Topics

    • Christian Kuehn
    Pages 619-663

About this book

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.

Keywords

  • Bifurcations
  • Canards
  • Fast-Slow Systems
  • Geometric Singular Perturbation Theory
  • Invariant Manifolds
  • Mixed-mode Oscillations
  • Multiple Time Scales
  • Normal Hyperbolicity
  • ordinary differential equations

Reviews

“It merges a wide variety of different mathematical techniques into a more unified framework. … this is a very interesting introduction to multiscale dynamics which will be of much assistance to both students and researchers. The target audience of this book is senior undergraduates and graduate students as well as researchers interested in using the theory of multiple time scale dynamics in nonlinear science, either from a theoretical or a mathematical modeling perspective.” (Tewfik Sari, Mathematical Reviews, May, 2016)

“This interesting monograph is a self-contained, coherent overview of the backgrounds and progress of the dynamical systems with multiple time scales. … The book contains excellent mathematics and is a well-written and unique source of information on the multiple time scale dynamics. I highly recommend it to all researchers and graduate students who would like to understand the geometric singular perturbation theory.” (Robert Vrabel, zbMATH 1335.34001, 2016)

Authors and Affiliations

  • Institute for Analysis and SC and Scientific Computing, Vienna University of Technology, Vienna, Austria

    Christian Kuehn

About the author

Christian Kuehn is a Postdoctoral Researcher at Vienna University of Technology, Institute for Analysis and Scientific Computing in Vienna, Austria.  He received his PhD in Applied Mathematics from Cornell University in 2010.  His research areas include: applied mathematics, differential equations, dynamical systems, numerical mathematics, and stochastics.

Bibliographic Information

Buying options

eBook USD 29.99 USD 59.99
50% discount Price excludes VAT (USA)
  • ISBN: 978-3-319-12316-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 39.99 USD 79.99
50% discount Price excludes VAT (USA)
Hardcover Book USD 59.99 USD 119.99
50% discount Price excludes VAT (USA)