Snaking of Multiple Homoclinic Orbits in Reversible Systems

We study N -homoclinic orbits near a heteroclinic cycle in a reversible system. The cycle is assumed to connect two equilibria of saddle-focus type. Using Lin’s method we establish the existence of infinitely many N -homoclinic orbits for each N near the cycle. In particular, these orbits exist along snaking curves, thus mirroring the behaviour one-homoclinic orbits. The general analysis is illustrated by numerical studies for a Swift-Hohenberg system.