Nature of synchronization transitions in random networks of coupled oscillators.

We consider a system of phase oscillators with random intrinsic frequencies coupled through sparse random networks and investigate how the connectivity disorder affects the nature of collective synchronization transitions. Various distribution types of intrinsic frequencies are considered: uniform, unimodal, and bimodal distribution. We employ a heterogeneous mean-field approximation based on the annealed networks and also perform numerical simulations on the quenched Erdös-Rényi networks. We find that the connectivity disorder drastically changes the nature of the synchronization transitions. In particular, the quenched randomness completely wipes away the diversity of the transition nature, and only a continuous transition appears with the same mean-field exponent for all types of frequency distributions. The physical origin of this unexpected result is discussed.