论文标题
具有高阶相互作用的网络动力学：相同细胞和同步的耦合细胞超网
Network Dynamics with Higher-Order Interactions: Coupled Cell Hypernetworks for Identical Cells and Synchrony
论文作者
论文摘要
在两个以上节点状态下非线性的网络交互（也称为高阶交互）可能会对集体网络动态产生深远的影响。在这里，我们开发了一个耦合的单元格式形式主义，以阐明具有高阶相互作用的网络动力学系统中（群集）同步模式的存在和稳定性。更具体地说，我们为耦合的细胞超网定义了强大的同步子空间，其耦合结构由基础超图确定，并描述了一般性超网络的那些空间。由于可以将超电绘制为在其节点和超息之间的两分图等效，因此我们将超网络的同步子空间与相应发病率挖掘的平衡着色相关联。
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.
