Synchronization Conditions of a Mixed Kuramoto Ensemble in Attractive and Repulsive Couplings

被引：3

作者：

Ha, Seung-Yeal ^{[1
,2
,3
]}

Kim, Dohyun ^{[4
]}

Lee, Jaeseung ^{[5
]}

Noh, Se Eun ^{[6
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

[3] Korea Inst Adv Study, Hoegiro 85, Seoul 02455, South Korea

[4] Sungshin Womens Univ, Sch Math Stat & Data Sci, Seoul 02844, South Korea

[5] Samsung Elect Co, Ctr Artificial Intelligence, Samsung Res, 56 Seongchon Gil, Seoul 06765, South Korea

[6] Myongji Univ, Dept Math, Yongin 17058, South Korea

来源：

JOURNAL OF NONLINEAR SCIENCE | 2021年 / 31卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Attractive– repulsive coupling; Inertial Kuramoto model; Kuramoto model; Synchronization; POWER GRIDS; SYSTEMS; STABILITY; OSCILLATORS; CONVERGENCE; MODEL; POPULATIONS; DYNAMICS;

D O I：

10.1007/s00332-021-09699-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the emergent dynamics of a mixed Kuramoto ensemble in the presence of both attractive and repulsive coupling strengths. To be precise, we consider coupled Kuramoto-type systems consisting of two ensembles in which the oscillators in the same group interact attractively with a positive intra-group coupling strength, whereas the oscillators in the different group communicate repulsively with a negative inter-group coupling strength. For the modeling perspective of the Kuramoto model (KM for brevity), two types of systems are treated in this paper: an attractive-repulsive inertial KM-KM and an attractive-repulsive KM-KM. For these two models, we provide sufficient frameworks leading to complete bi-polar synchronization in which asymptotic configuration tends to a bi-polar state. Our estimates mainly rely on the gradient-like flow formulation and the energy estimate.

引用

页数：34

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