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Geometric Singular Perturbation Theory Beyond the Standard Form

  • Martin Wechselberger
Book

Part of the Frontiers in Applied Dynamical Systems: Reviews and Tutorials book series (FIADS, volume 6)

Table of contents

  1. Front Matter
    Pages i-x
  2. Martin Wechselberger
    Pages 1-4
  3. Martin Wechselberger
    Pages 5-39
  4. Martin Wechselberger
    Pages 41-60
  5. Martin Wechselberger
    Pages 61-75
  6. Martin Wechselberger
    Pages 77-91
  7. Martin Wechselberger
    Pages 93-125
  8. Martin Wechselberger
    Pages 127-130
  9. Back Matter
    Pages 131-137

About this book

Introduction

This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT).

It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form

The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. 

Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.


Keywords

multiple scales singular perturbations differential equations invariant manifolds Fenichel Theory Canard Theory biochemical reactions relaxation oscillators

Authors and affiliations

  • Martin Wechselberger
    • 1
  1. 1.School of Mathematics and StatisticUniversity of SydneySydneyAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-36399-4
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-36398-7
  • Online ISBN 978-3-030-36399-4
  • Series Print ISSN 2364-4532
  • Series Online ISSN 2364-4931
  • Buy this book on publisher's site
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