高阶交互作用下复用网络的层内和层间同步
Intralayer and interlayer synchronization in multiplex network with higher-order interactions
摘要：
复杂系统的最新发展已经证明，许多真实世界的场景，成功地表示为网络并不总是限于二进制的相互作用，但往往包括更高阶的节点之间的相互作用。这些超越成对交互优选地由超图建模，其中超边表示一组节点之间的高阶交互。在这项工作中，我们考虑了一个多路复用网络的层内连接表示的超图，称为多路复用超图。超图是通过将无标度网络的最大团映射到适当大小的超边来构造的。我们研究了这种多重结构的层内和层间同步。我们的研究揭示了当考虑高阶结构时，尽管只有成对连接，层内同步明显增强。利用主稳定性函数方法得到了同步态稳定的必要条件，与数值结果完全一致。我们还探讨了层间同步的鲁棒性，发现对于多体相互作用的多重网络，层间同步比成对相互作用的多重网络更持久。
英文摘要：
Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These beyond pairwise interactions are preferably modeled by hypergraphs, where hyperedges represent higher-order interactions between a set of nodes. In this work, we consider a multiplex network where the intralayer connections are represented by hypergraphs, called multiplex hypergraph. The hypergraph is constructed by mapping the maximal cliques of a scale-free network to hyperedges of suitable sizes. We investigate the intralayer and interlayer synchronization of such multiplex structures. Our study unveils that the intralayer synchronization appreciably enhances when the higher-order structure is taken into consideration inspite of only pairwise connections. We derive the necessary condition for stable synchronization states by the master stability function approach, which perfectly agrees with the numerical results. We also explore the robustness of interlayer synchronization and find that for the multiplex structures with many-body interaction, the interlayer synchronization is more persistent than multiplex networks with pairwise interaction.
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