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Titlebook: Geometric Singular Perturbation Theory Beyond the Standard Form; Martin Wechselberger Book 2020 The Editor(s) (if applicable) and The Auth

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发表于 2025-3-21 18:29:17 | 显示全部楼层 |阅读模式
书目名称Geometric Singular Perturbation Theory Beyond the Standard Form
编辑Martin Wechselberger
视频video
概述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.Cove
丛书名称Frontiers in Applied Dynamical Systems: Reviews and Tutorials
图书封面Titlebook: Geometric Singular Perturbation Theory Beyond the Standard Form;  Martin Wechselberger Book 2020 The Editor(s) (if applicable) and The Auth
描述.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 & Statist
出版日期Book 2020
关键词multiple scales; singular perturbations; differential equations; invariant manifolds; Fenichel Theory; Ca
版次1
doihttps://doi.org/10.1007/978-3-030-36399-4
isbn_softcover978-3-030-36398-7
isbn_ebook978-3-030-36399-4Series ISSN 2364-4532 Series E-ISSN 2364-4931
issn_series 2364-4532
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Pseudo Singularities and Canards,utputs under system parameter variations. The time-scale splitting in our singular perturbation problems creates additional complexity and sometimes surprising, counter-intuitive behaviour. We start with a couple of examples to motivate the development of the corresponding theory.
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https://doi.org/10.1057/9781137315762utputs under system parameter variations. The time-scale splitting in our singular perturbation problems creates additional complexity and sometimes surprising, counter-intuitive behaviour. We start with a couple of examples to motivate the development of the corresponding theory.
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Introduction,s reflect these multiple-scale features as well. Mathematical models of such multiple-scale systems are considered singular perturbation problems with two-scale problems as the most prominent. Singular perturbation theory studies systems featuring a small perturbation parameter reflecting the scale
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Loss of Normal Hyperbolicity,tem to switch between slow and fast dynamics as observed in many relaxation oscillator models; see Chap. .. Geometrically, loss of normal hyperbolicity occurs generically along (a union of) codimension-one submanifold(s) of . where a nontrivial eigenvalue of the layer problem crosses the imaginary a
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Pseudo Singularities and Canards,o far: .Partial answers to the above questions can be found in classic . [.] which focuses on understanding significant changes in dynamical systems outputs under system parameter variations. The time-scale splitting in our singular perturbation problems creates additional complexity and sometimes s
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