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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Motivating Examples,In this chapter we present models that fall under the category of standard singularly perturbation systems (.), respectively, (.) as well as less known variants of these models that are of the general form (.), respectively, (.).

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A Coordinate-Independent Setup for GSPT,This chapter is devoted to present a geometric approach to singular perturbation theory for ordinary differential equations. The material is based on Fenichel’s seminal work on . with a particular emphasis on his coordinate-independent approach (see [.], Sections 5–9).

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What We Did Not Discuss,Finally, we briefly mention a few selected topics on GSPT that have not been covered in this manuscript. This list of topics is non-inclusive—it is an author’s choice (like all topics covered in this manuscript).

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978-3-030-36398-7The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Hongbo Ren,Weisheng Zhou,Xuepeng Qians 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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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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https://doi.org/10.1057/9781137315762o 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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