Collective-phase description of coupled oscillators with general network structure.

We develop a collective-phase description for a population of nonidentical limit-cycle oscillators with any network structure undergoing fully phase-locked collective oscillations. The whole network dynamics can be described by a single collective-phase variable. We derive a general formula for the collective-phase sensitivity, which quantifies the phase response of the whole network to weak external perturbations applied to the constituent oscillators. Moreover, we consider weakly interacting multiple networks and develop an effective phase coupling description for them. Several examples are given to illustrate our theory.