Abstract

We consider large populations of phase oscillators with maximal heterogeneity in interactions - allcoupling functions are taken randomly from some distribution. We show that upon a reasonable assumption of independence of the interactions and the phases, one can transform the dynamics to an effective homogeneous ensemble with averaged coupling functions. Examples include cases where the randomness enters the coupling strengths and the phase shifts. Furthermore, we analyze the situation with full frustration due to a uniform distribution of the phase shifts in the coupling. Here a subtle transition to partial synchrony is observed, description of which requires introduction of a novel correlation order parameter.