具有高阶相互作用的网络动力学：用于相同单元与同步的耦合单元超网络
Network Dynamics with Higher-Order Interactions: Coupled Cell Hypernetworks for Identical Cells and Synchrony
AI总结：
本文开发了耦合单元超网络形式体系，通过定义鲁棒同步子空间并将其与关联有向图的平衡着色相联系，阐明了具有高阶相互作用的网络动力系统中簇同步模式的存在性与稳定性。
摘要：
在多于两个节点状态上呈非线性的网络相互作用——也称为高阶相互作用——能够对集体网络动力学产生深远影响。在此，我们开发了一种耦合单元超网络形式体系，以阐明具有高阶相互作用的网络动力系统中（簇）同步模式的存在性与稳定性。更具体地，我们为耦合结构由底层超图决定的耦合单元超网络定义了鲁棒同步子空间，并描述了一般此类超网络中的这些空间。由于超图可以等价地表示为其节点与超边之间的二部图，我们将超网络的同步子空间与相应关联有向图的平衡着色联系起来。
英文摘要：
Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to elucidate the existence and stability of (cluster) synchronization patterns in network dynamical systems with higher-order interactions. More specifically, we define robust synchrony subspace for coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph and describe those spaces for general such hypernetworks. Since a hypergraph can be equivalently represented as a bipartite graph between its nodes and hyperedges, we relate the synchrony subspaces of a hypernetwork to balanced colorings of the corresponding incidence digraph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
