The Geometry of Slow Manifolds near a Folded Node

M. Desroches, B. Krauskopf, H.M. Osinga

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

This paper is concerned with the geometry of slow manifolds of a dynamical system with one fast and two slow variables. Specifically, we study the dynamics near a folded-node singularity, which is known to give rise to so-called canard solutions. Geometrically, canards are intersection curves of two-dimensional attracting and repelling slow manifolds, and they are a key element of slow-fast dynamics. For example, canard solutions are associated with mixed-mode oscillations, where they organize regions with different numbers of small oscillations. We perform a numerical study of the geometry of two-dimensional slow manifolds in the normal form of a folded node in ℝ
Original languageEnglish
Pages (from-to)1131-1162
Number of pages32
JournalSIAM Journal on Applied Dynamical Systems
Volume7
Issue number4
Early online date13 Oct 2008
DOIs
Publication statusPublished - 2008

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