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Frontiers in Applied Dynamical Systems: Reviews and Tutorials

Geometric Singular Perturbation Theory Beyond the Standard Form

Authors: Wechselberger, Martin

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  • First of its kind to discuss geometric singular perturbation theory in a coordinate-independent setting
  • Serves as an accessible entry point into the study of multiple time-scale dynamical systems
  • Covers motivating examples from biochemistry, electronic circuits and mechanic oscillators and advection-reaction-diffusion problems
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About this book

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.


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $59.99
price for Mexico (gross)
  • ISBN 978-3-030-36399-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for Mexico
  • ISBN 978-3-030-36398-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Singular Perturbation Theory Beyond the Standard Form
Authors
Series Title
Frontiers in Applied Dynamical Systems: Reviews and Tutorials
Series Volume
6
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-36399-4
DOI
10.1007/978-3-030-36399-4
Softcover ISBN
978-3-030-36398-7
Series ISSN
2364-4532
Edition Number
1
Number of Pages
X, 137
Number of Illustrations
2 b/w illustrations, 40 illustrations in colour
Topics

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