Blowup for flat slow manifolds: Paper

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Abstract

In this paper, we present a way of extending the blowup method, in the formulation of Krupa and Szmolyan, to flat slow manifolds that lose hyperbolicity beyond any algebraic order. Although these manifolds have infinite co-dimensions, they do appear naturally in certain settings; for example, in (a) the regularization of piecewise smooth systems by tanh, (b) a particular aircraft landing dynamics model, and finally (c) in a model of earthquake faulting. We demonstrate the approach using a simple model system and the examples (a) and (b).
Original languageEnglish
JournalNonlinearity
Volume30
Issue number5
Pages (from-to)2138-2184
ISSN0951-7715
DOIs
Publication statusPublished - 2017

Keywords

  • Blowup
  • Slow-fast systems
  • Geometric singular perturbation theory

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