Effects of core-periphery structure on explosive synchronization

Abstract

We investigate the explosive synchronization in networks with core-periphery structure. The effects of different patterns of core-periphery networks on explosive synchronization are studied by altering network structural parameters. With the variation of two core-periphery structural parameters, the relative connection strength between core and peripheral nodes, and the relative connection strength among peripheral nodes, we find distinct roles played by structural parameters in the path toward explosive synchronization. Our results show that the order parameter of periphery is closer to that of the core in the synchronization phase with the increment of connections between core and peripheral nodes. In addition, we find that sparser the connections among peripheral nodes are, the easier the whole dynamic network is to reach explosive synchronization. We also discover that if the number of connections between core and periphery scales vary sublinearly with the network size, there exists a novel two-jump behavior of the order parameter of the whole network. Moreover, as the level of the sublinearity increases, the order parameter starts to oscillate in a decaying manner, rather than being increasing monotonically and slowly as in the case of normal explosive synchronization when the coupling strength exceeds a critical threshold. Hence in this regime, it becomes increasingly difficult for the network to maintain stable explosive synchronization even though the underlying network topology is connected.