Onset of chaotic phase synchronization in complex networks of coupled heterogeneous oscillators

Existing studies on network synchronization focused on complex networks possessing either identical or nonidentical but simple nodal dynamics. We consider networks of both complex topologies and heterogeneous but chaotic oscillators, and investigate the onset of global phase synchronization. Based on a heuristic analysis and by developing an efficient numerical procedure to detect the onset of phase synchronization, we uncover a general scaling law, revealing that chaotic phase synchronization can be facilitated by making the network more densely connected. Our methodology can find applications in probing the fundamental network dynamics in realistic situations, where both complex topology and complicated, heterogeneous nodal dynamics are expected.