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＜電子ブック＞
Geometric Singular Perturbation Theory Beyond the Standard Form / by Martin Wechselberger
(Frontiers in Applied Dynamical Systems: Reviews and Tutorials. ISSN:23644931 ; 6)

版	1st ed. 2020.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2020
大きさ	X, 137 p. 42 illus., 40 illus. in color : online resource
著者標目	*Wechselberger, Martin author SpringerLink (Online service)
件　名	LCSH:Dynamical systems LCSH:Operator theory LCSH:Differential equations FREE:Dynamical Systems FREE:Operator Theory FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-36399-4

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