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Geometric Singular Perturbation Theory Beyond the Standard Form

por Martin Wechselberger
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60,87 €
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Martin Wechselberger Geometric Singular Perturbation Theory Beyond the Standard Form
Martin Wechselberger - Geometric Singular Perturbation Theory Beyond the Standard Form

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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.


Martin Wechselberger

Detalles de producto

X, 137 p. 42 illus., 40 illus. in color.
Introduction.- Motivating examples.- A coordinate-independent setup for GSPT.- Loss of normal hyperbolicity.- Relaxation oscillations in the general setting.- Pseudo singularities & canards.- What we did not discuss.
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

Tipo de medio:
Tapa blanda
Springer International Publishing
1st ed. 2020
Número de páginas:

Datos base

Tipo de producto:
Libro de bolsillo
Dimensiones del paquete:
0.234 x 0.154 x 0.01 m; 0.18 kg
60,87 €
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