Extension of synchronizability analysis based on vital factors: Extending validity to multilayer fully coupled networks

In this paper, we study the synchronizability of multilayer fully coupled networks and their simplest equivalent networks and then discuss the vital factors affecting the synchronizability. First, we use the master stability method to theoretically deduce the synchronizability of a multilayer fully coupled network and its simplest equivalent network. It is proven that a multilayer fully coupled network has the same synchronizability as its corresponding simplest equivalent network. Second, we conduct experiments to verify the derivation and observe the process of synchronization. Finally, we analyze the factors affecting the synchronizability of multilayer fully coupled networks. The five influencing factors are identified as the intralayer coupling strength, the interlayer coupling strength, the number of nodes in each network layer, the number of vital nodes and the number of layers in the network. The current findings allow us to gain a deeper understanding of the synchronization behavior and properties of real-world networks. (C) 2020 Elsevier Ltd. All rights reserved.