The relationship between the topology and synchronizability of partially interdependent networks

Abstract

Based on the master stability function method, some theoretical results are derived for the synchronizability of partially interdependent networks. For bounded and unbounded synchronous regions and three different kinds of inter-coupling, we illustrate how factors of the topology can affect the synchronizability of networks with a Barabási-Albert (BA) scale-free and a Newman-Watts (NW) small-world subnet (simplified here as BA-NW network) and networks with a BA scale-free and a nearest-neighbor (NN) subnet (BA-NN network), respectively. When only the scale of the networks is increased, the synchronizability systematically reduces. If only increasing the inter-coupling strength or the number of interdependent nodes, the synchronizability keeps improving. Generally, we find that BA-NW networks have better synchronizability than BA-NN networks and positively correlated coupling is the best interconnection. Random inter-coupling, by contrast, is the best choice for BA-NN networks.