Dynamics near a periodically forced robust heteroclinic cycle

In this article we discuss, with a combination of analytical and numerical results, a canonical set of differential equations with a robust heteroclinic cycle, subjected to time-periodic forcing. We find that three distinct dynamical regimes exist, depending on the ratio of the contracting and expanding eigenvalues at the equilibria on the heteroclinic cycle which exists in the absence of forcing. By reducing the dynamics to that of a two dimensional map we show how frequency locking and complex dynamics arise.