论文标题
全球拓扑和细胞复合物上的全球拓扑同步
Global topological synchronization on simplicial and cell complexes
论文作者
论文摘要
拓扑信号，即高阶网络的节点，链接，三角形等定义的动力学变量，正在吸引越来越多的注意力。但是，对他们的集体现象的调查仅尚处于起步阶段。在这里，我们结合拓扑和非线性动力学，以确定在简单或细胞复合物上定义的拓扑信号的全局同步条件。在简单复合物上，我们表明拓扑阻塞阻碍了奇数信号在全球同步。另一方面，我们表明细胞复合物可以克服拓扑阻塞，在某些结构中，任何维度的信号都可以实现全局同步。
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we combine topology and nonlinear dynamics to determine the conditions for global synchronization of topological signals defined on simplicial or cell complexes. On simplicial complexes we show that topological obstruction impedes odd dimensional signals to globally synchronize. On the other hand, we show that cell complexes can overcome topological obstruction and in some structures, signals of any dimension can achieve global synchronization.
