In this study, we consider a simple NoN consisting of two coupled subnetworks and examine the effect of the topology of the subnetworks on the global synchrony. The topologies we consider are: random; SW; SF; and “super-hub,” which is characterized by the presence of a few hub nodes that are fully connected to all other nodes. Each node is represented as a Kuramoto phase oscillator, and the synchronization is evaluated by calculating the Kuramoto order parameter, r. We evaluate the networks in terms of the minimum coupling strength necessary to achieve synchronized state, by analyzing the minimum inter-node coupling strength necessary for r to exceed a threshold value. In the current study, the threshold was set to be r = 0.9. We show that in networks of heterogenous phase oscillators, the optimal topology varies between a single network and a NoN. Finally, we consider a NoN with three subnetworks and evaluate how coupling schemes between subnetworks of different mean frequencies affect the global synchrony.
