Synchronizability of multi-layer small-world dynamical networks

This paper investigates the synchronizability of multi-layer small-world dynamical networks and discusses the significant factors affecting the synchronizability. First, we introduce the network model of multi-layer small-world dynamical networks with one-to-one connections in the inter-layer connections and each layer has the same topology. Second, we consider the topological parameters including adding probability, intra-layer coupling strength, inter-layer coupling strength, number of nodes per layer, initial node degree, and number of network layers which will influence the network's synchronizability. Third, we adopt the master stability function method and numerical simulations to analyze the synchronizability of the network. We also examine how the topological parameters influence the synchronizability of multi-layer small-world dynamical networks and the relationships among these parameters. Finally, synchronization control experiments are conducted to verify our results. As a result, we find that only increasing the number of nodes per layer will weaken the synchronizability of multi-layer small-world dynamical networks, while increasing other topological parameters will enhance the synchronizability. The current findings enable us to gain a deeper understanding of the synchronization behavior and characteristics of multi-layer small-world dynamical networks.