High frequency forcing of an attracting heteroclinic cycle

Abstract

This article is concerned with the effect of time-periodic forcing on a vector field exhibiting an attracting heteroclinic network. We show that as the forcing frequency tends to infinity, the dynamics reduces to that of a network under constant forcing, the constant being the average value of the forcing term. We also show that under small constant forcing the network breaks up into an attracting periodic solution that persists for periodic forcing of high frequency.