论文标题
超图上的耦合动力学：稳态的主稳定性和同步
Coupled Dynamics on Hypergraphs: Master Stability of Steady States and Synchronization
论文作者
论文摘要
在网络/图形上动态系统的研究中，一个关键主题是网络拓扑如何影响稳态或同步状态的稳定性。理想情况下，人们希望得出稳定性或不稳定性的条件，这些条件不是单个节点/顶点的微观细节，而是使网络耦合拓扑的影响可见。主稳定性功能是实现此目标的重要工具。在这里，我们将主稳定性方法推广到超图。超图耦合结构很重要，因为它使我们可以考虑节点之间的任意高阶相互作用。例如，在耦合地图晶格的理论中，我们详细研究了拉普拉斯类型的相互作用结构。由于超图上的拉普拉斯人的光谱理论比图表上的频谱理论更丰富，因此我们看到了新的动态现象的可能性。更一般而言，我们的参数为如何概括从图表到超图的动力结构和结果提供了蓝图。
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that instead of microscopic details of the individual nodes/vertices rather make the influence of the network coupling topology visible. The master stability function is an important such tool to achieve this goal. Here we generalize the master stability approach to hypergraphs. A hypergraph coupling structure is important as it allows us to take into account arbitrary higher-order interactions between nodes. As for instance in the theory of coupled map lattices, we study Laplace type interaction structures in detail. Since the spectral theory of Laplacians on hypergraphs is richer than on graphs, we see the possibility of new dynamical phenomena. More generally, our arguments provide a blueprint for how to generalize dynamical structures and results from graphs to hypergraphs.
