On synchronization of the double sphere Kuramoto model with connected undirected graphs

被引：3

作者：

Shi, Yushi ^{[1
,2
]}

Li, Ting ^{[1
]}

Zhu, Jiandong ^{[1
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Nanjing, Peoples R China

[2] Nanjing Univ Sci & Technol, Zijin Coll, Nanjing, Peoples R China

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2023年 / 443卷

关键词：

Double sphere Kuramoto model; Synchronization; Synchronization rate; Undirected graph; OSCILLATORS;

D O I：

10.1016/j.physd.2022.133555

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

M.A. Lohe first proposed the double sphere Kuramoto model (On the double sphere model of synchronization, Physica D: Nonlinear Phenomena, 412:132642, 2020), which is a more general model than the high-dimensional Kuramoto model defined on a sphere. For the double sphere Kuramoto model with a complete graph, some theoretic results on synchronization were obtained. But for the case of general graphs, there is no report yet. In this paper, for the double sphere Kuramoto model composed of identical oscillators interacting through a connected undirected graph with a symmetric nonnegative adjacency matrix, the synchronization is proved by using LaSalle's invariance principle. Moreover, the exponential synchronization is achieved, and the supremum of exponential synchronization rates is exactly obtained.(c) 2022 Elsevier B.V. All rights reserved.

引用

页数：8

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