Geometric singular perturbation theory beyond the standard form
- 作者： Wechselberger, Martin, author.
- 其他作者：
- 其他題名：
- Frontiers in applied dynamical systems: reviews and tutorials ;
- 出版： Cham : Springer International Publishing :Imprint: Springer
- 叢書名： Frontiers in applied dynamical systems: reviews and tutorials,volume 6
- 主題： Singular perturbations (Mathematics) , Dynamical Systems and Ergodic Theory. , Operator Theory. , Ordinary Differential Equations.
- ISBN： 9783030363994 (electronic bk.) 、 9783030363987 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: 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.
- 摘要註: 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.
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讀者標籤：
- 系統號： 005481576 | 機讀編目格式
館藏資訊
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.