Abstract
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 behavior of 1-homoclinic orbits. The general analysis is illustrated by numerical studies for a Swift–Hohenberg system.
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