Clustering and slow switching in globally coupled phase oscillators

Abstract

We consider a network of globally coupled phase oscillators. The interaction between any two of them is derived from a simple model of weakly coupled biological neurons and is a periodic function of the phase difference with two Fourier components. The collective dynamics of this network is studied with emphasis on the existence and the stability of clustering states. Depending on a control parameter, three typical types of dynamics can be observed at large time: a fully synchronized state of the network (one-cluster state), a totally incoherent state, and a pair of two-cluster states connected by heteroclinic orbits. This last regime is particularly sensitive to noise. Indeed, adding a small noise gives rise, in large networks, to a slow periodic oscillation between the two two-cluster states. The frequency of this oscillation is proportional to the logarithm of the noise intensity. These switching states should occur frequently in networks of globally coupled oscillators.