论文标题
具有无限许多稳定平衡的库拉莫托网络
Kuramoto Networks with Infinitely Many Stable Equilibria
论文作者
论文摘要
我们证明，图上的库拉莫托模型可以包含无限的许多非等效稳定平衡。更确切地说，我们证明，对于每个正整数D，都有一个连接的图，使得稳定平衡的集合包含尺寸d的多种形式。特别是，我们解决了R. Delabays，T。Coletta和P. Jacquod的猜想，内容涉及平面图上的平衡数量。我们的结果基于平衡配置的分析，该配置对应于拓扑中的等边性多边形链接。为了分析平衡流形的稳定性，我们采用拓扑分叉理论。
We prove that the Kuramoto model on a graph can contain infinitely many non-equivalent stable equilibria. More precisely, we prove that for every positive integer d there is a connected graph such that the set of stable equilibria contains a manifold of dimension d. In particular, we solve a conjecture of R. Delabays, T. Coletta and P. Jacquod about the number of equilibria on planar graphs. Our results are based on the analysis of balanced configurations, which correspond to equilateral polygon linkages in topology. In order to analyze the stability of manifolds of equilibria we apply topological bifurcation theory.
