Kuramoto Networks with Infinitely Many Stable Equilibria

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-30 DOI:10.1137/23m155400x

Davide Sclosa

引用次数: 3

Abstract

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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具有无穷多稳定平衡点的Kuramoto网络

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.