Computation of saddle-type slow manifolds using iterative methods

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Abstract

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, which require mesh refinements to ensure uniform convergence with respect to , appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples, including a model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables, and the computation of homoclinic connections in the FitzHugh–Nagumo system.
Original languageEnglish
JournalS I A M Journal on Applied Dynamical Systems
Volume14
Issue number2
Pages (from-to)1189–1227
ISSN1536-0040
DOIs
Publication statusPublished - 2015

Keywords

  • Slow-fast systems
  • Slow manifolds of saddle type
  • Reduction methods

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