Periodic solutions and slow manifolds

Abstract

After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we discuss a 4-dimensional relaxation oscillation and also canardlike solutions emerging from the modified logistic equation with sign-alternating growth rates.