Heteroclinic Ratchets in a System of Four Coupled Oscillators

Abstract

We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. We show that the system can have a robust attractor that responds to a specific detuning between certain pairs of the oscillators by a breaking of phase locking for arbitrary positive detunings but not for negative detunings. As the dynamical mechanism behind this is a particular type of heteroclinic network, we call this a 'heteroclinic ratchet' because of its dynamical resemblance to a mechanical ratchet.