Slow–fast n-dimensional piecewise linear differential systems

Abstract

In this article we analyze n-dimensional slow–fast systems in a piecewise linear framework. In particular, we prove a Fenichel's-like Theorem where we give an explicit expression for the invariant slow manifold, that leads to the proof of the existence and location of maximal canards orbits. We show that these orbits perturb from singular orbits through contact points, of order greater than or equal to two, between the reduced flow and the fold manifold. In the particular case n=3, we show that the unique contact point is a visible two-fold singularity.