A novel approach to synchronization in coupled excitable systems

Abstract

We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically that the collective oscillations persist in a large region in parameter. For a regular topology with \emph{few} connections between the oscillators, islands of coherent oscillations are formed, which merge as the amount of topological disorder increases. We link this transition to typical network quantities in the framework of small-world networks.