Synchronization in a Kuramoto mean field game

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2023-09-02 DOI:10.1080/03605302.2023.2264611

Rene Carmona, Quentin Cormier, H. Mete Soner

引用次数: 6

Abstract

AbstractThe classical Kuramoto model is studied in the setting of an infinite horizon mean field game. The system is shown to exhibit both synchronization and phase transition. Incoherence below a critical value of the interaction parameter is demonstrated by the stability of the uniform distribution. Above this value, the game bifurcates and develops self-organizing time homogeneous Nash equilibria. As interactions get stronger, these stationary solutions become fully synchronized. Results are proved by an amalgam of techniques from nonlinear partial differential equations, viscosity solutions, stochastic optimal control and stochastic processes.KEYWORDS: Mean field gamesKuramoto modelsynchronizationviscosity solutions2020 MATHEMATICS SUBJECT CLASSIFICATION: 35Q8935D4039N8091A1692B25 Additional informationFundingResearch of Carmona was partially supported by AFOSR FA9550-19-1-0291 and ARPA-E DE-AR0001289. Research of Soner was partially supported by the National Science Foundation grant DMS 2106462.

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Kuramoto平均场博弈中的同步

摘要研究了无限视界平均场对策下的经典Kuramoto模型。该系统显示出同步和相变。均匀分布的稳定性证明了在相互作用参数临界值以下的非相干性。在此值以上，博弈分叉并发展为自组织时间齐次纳什均衡。当相互作用变得更强时，这些固定的解变得完全同步。结果由非线性偏微分方程、粘度解、随机最优控制和随机过程的综合技术证明。关键词:平均场游戏kuramoto模型同步粘度解2020数学学科分类:35Q8935D4039N8091A1692B25附加信息卡莫纳的研究得到了AFOSR FA9550-19-1-0291和ARPA-E DE-AR0001289的部分资助。Soner的研究得到了国家科学基金项目DMS 2106462的部分支持。

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来源期刊

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.