CLUSTERING AND SLOW SWITCHING IN GLOBALLY COUPLED PHASE OSCILLATORS

We consider a network of globally coupled phase oscillators. The inter action between any two of them is derived from a simple model of weakl y coupled biological neurons and is a periodic function of the phase d ifference with two Fourier components. The collective dynamics of this network is studied with emphasis on the existence and the stability o f clustering states. Depending on a control parameter, three typical t ypes of dynamics can be observed at large time: a fully synchronized s tate of the network (one-cluster state), a totally incoherent state, a nd a pair of two-cluster states connected by heteroclinic orbits. This last regime is particularly sensitive to noise. Indeed, adding a smal l 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 switchi ng states should occur frequently in networks of globally coupled osci llators.