论文标题
多路复用网络中具有高阶相互作用的内层和层间同步
Intralayer and interlayer synchronization in multiplex network with higher-order interactions
论文作者
论文摘要
复杂系统中的最新发展目睹了许多现实世界的场景成功地表示为网络，并不总是局限于二进制相互作用，但通常包括节点之间的高阶相互作用。这些超出成对相互作用优选由超图建模，其中超蛋白质代表一组节点之间的高阶相互作用。在这项工作中，我们考虑了一个多路复用网络，其中内部连接由HyperGraphs表示，称为Multiplex HyperGraph。通过将无秤网络的最大簇映射到合适尺寸的超钢中，构建了超图。我们研究了这种多重结构的内层和层间同步。我们的研究揭示了当仅考虑成对连接的情况下，在考虑到高阶结构时，内部同步会显着增强。我们通过主稳定函数方法得出了稳定同步状态的必要条件，这与数值结果完全一致。我们还探讨了层中同步的鲁棒性，并发现对于具有多体相互作用的多重结构，层间同步比具有成对相互作用的多重网络更持久。
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.
