Synchronous Stability in Multiplex Network Subject to Higher-Order Intralayer Interactions

Recent research and instances have demonstrated that most real-world systems can be effectively schematized by multiplex networks. Moreover, the interactions within systems often emerge among triadic or tetradic interactions, or even interactions with more element combinations, in addition to pairwise interactions. Hypergraph coupling structures are particularly well-suited for capturing such arbitrary higher-order interactions among nodes, thereby playing a key role in accurately depicting system dynamics. Meanwhile, the functionality of numerous complex systems depends on synchronization mechanisms. Therefore, this paper focuses on investigating the synchronous stability of a multiplex hypergraph. Specifically, we examine a three-layer network where intralayer interactions are represented by hyperedges, while the interlayer interactions are modeled through pairwise couplings. By generalizing the master stability function approach to the hypergraph structure, the synchronization phenomenon of such multiplex hypergraphs is analyzed. To verify our theoretical conclusions, we apply the proposed framework to networks of FitzHugh–Nagumo neurons and Rikitake two-disk dynamos. Simulation results unveil that the presence of higher-order interactions enhances the synchronous ability within the multiplex framework.