Explosive synchronization on co-evolving networks

Many realistic dynamics are based on complicated networks such as the co-evolving networks with mutual correlation, in contrast to the recent focus on single- or multi-layered networks. We here study this kind of realistic dynamics by presenting a network model consisting of two interdependent subnetworks, which have the same power-law degree distribution. We focus on the dynamics of explosive synchronization. We show that the explosive synchronization can exist for a large class of co-evolving networks with scale-free distributions, thus extending the condition of explosive synchronization from strong correlation with w_i = k_i to weak correlation with w_i = f(k_i).