具有无穷多稳定平衡点的Kuramoto网络

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-11-30 DOI:10.1137/23m155400x

Davide Sclosa

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引用次数: 3

摘要

应用动力系统学报，vol . 22, Issue 4, Page 3267-3283, December 2023。摘要。证明了图上的Kuramoto模型可以包含无穷多个非等价稳定平衡点。更准确地说，我们证明了对于每一个[数学]存在一个连通图，使得稳定均衡集包含一个维数[数学]的流形。特别地，我们解决了Delabays, Coletta和Jacquod关于平面图上平衡点数目的猜想。我们的结果是基于平衡构型的分析，它对应于拓扑中的等边多边形连杆。为了分析平衡流形的稳定性，我们应用了拓扑分岔理论。

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Kuramoto Networks with Infinitely Many Stable Equilibria

SIAM Journal on Applied Dynamical Systems, Volume 22, Issue 4, Page 3267-3283, December 2023.
Abstract. We prove that the Kuramoto model on a graph can contain infinitely many nonequivalent stable equilibria. More precisely, we prove that for every [math] there is a connected graph such that the set of stable equilibria contains a manifold of dimension [math]. In particular, we solve a conjecture of Delabays, Coletta, and 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.

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来源期刊

SIAM Journal on Applied Dynamical Systems 物理-物理：数学物理

CiteScore

3.60

自引率

4.80%

发文量

审稿时长

6 months

期刊介绍： SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles on the mathematical analysis and modeling of dynamical systems and its application to the physical, engineering, life, and social sciences. SIADS is published in electronic format only.