The Geometry of Slow Manifolds near a Folded Node

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