We study explosive synchronization, a phenomenon characterized by first-order phase transitions between incoherent and synchronized states in networks of coupled oscillators. While explosive synchronization has been the subject of many recent studies, in each case strong conditions on the heterogeneity of the network, its link weights, or its initial construction are imposed to engineer a first-order phase transition. This raises the question of how robust explosive synchronization is in view of more realistic structural and dynamical properties. Here we show that explosive synchronization can be induced in mildly heterogeneous networks by the addition of quenched disorder to the oscillators' frequencies, demonstrating that it is not only robust to, but moreover promoted by, this natural mechanism. We support these findings with numerical and analytical results, presenting simulations of a real neural network as well as a self-consistency theory used to study synthetic networks.

• Received 3 April 2014

DOI:https://doi.org/10.1103/PhysRevE.89.062811