Overview
- 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
Part of the book series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials (FIADS, volume 6)
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Table of contents (7 chapters)
Keywords
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 tothe 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.
Authors and Affiliations
Bibliographic Information
Book Title: Geometric Singular Perturbation Theory Beyond the Standard Form
Authors: Martin Wechselberger
Series Title: Frontiers in Applied Dynamical Systems: Reviews and Tutorials
DOI: https://doi.org/10.1007/978-3-030-36399-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-36398-7Published: 22 February 2020
eBook ISBN: 978-3-030-36399-4Published: 21 February 2020
Series ISSN: 2364-4532
Series E-ISSN: 2364-4931
Edition Number: 1
Number of Pages: X, 137
Number of Illustrations: 2 b/w illustrations, 40 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Operator Theory, Ordinary Differential Equations