Robust Heteroclinic Behaviour, Synchronization, and Ratcheting of Coupled Oscillators

This review examines some recent work on robust heteroclinic networks that can appear as attractors for coupled dynamical systems. We focus on coupled phase oscillators and discuss a number of nonlinear dynamical phenomena that are atypical in systems without some coupling structure. The phenomena we discuss include heteroclinic cycles and networks between partially synchronized states. These networks can be attracting and robust to perturbations in parameters and system structure as long as the coupling structure is preserved. We discuss two related effects; extreme sensitivity to detuning (strongly coupled oscillators may lose their frequency synchrony for very small detunings) and heteroclinic ratchet where the sensitivity may only appear for detunings of one sign.