  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 either 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.
