Influence of Layer Similarity on the Synchronization of Multiplex Networks With Random Topologies
研究了随机拓扑多层网络中，层相似性如何影响网络同步，发现弱耦合下层相似性先促进后抑制同步，强耦合下抑制同步，而增加层数在强耦合时总是促进同步。
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.