Influence of Layer Similarity on the Synchronization of Multiplex Networks With Random Topologies

In this article, we study the synchronization of multiplex networks with random topologies and any number of layers. We propose a general framework for analyzing the synchronization of multiplex networks with or without layer similarity. Using random matrix theory, we obtain sufficient conditions of synchronization for multiplex networks under strong and weak interlayer coupling, respectively. We show, both analytically and numerically, that for weak interlayer coupling, increasing layer similarity can first promote synchronization and then hinder synchronization, while for strong interlayer coupling, synchronization can be suppressed. However, increasing the number of layers can always facilitate synchronization only if the interlayer coupling is strong. Finally, the theoretical results are verified by numerical simulations.