KURAMOTO ORDER PARAMETERS AND PHASE CONCENTRATION FOR THE KURAMOTO-SAKAGUCHI EQUATION WITH FRUSTRATION

被引：1

作者：

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

Morales, Javier ^{[4
]}

Zhang, Yinglong ^{[5
]}

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 87, Seoul 130722, South Korea

[4] Univ Maryland, Ctr Sci Computat & Math Modeling, College Pk, MD 20742 USA

[5] Korea Adv Inst Sci & Technol, Stochast Anal & Applicat Res Ctr, Daejeon 34141, South Korea

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 7-8期

基金：

新加坡国家研究基金会;

关键词：

Emergent dynamics; Kuramoto model; frustration; order parameters; synchronization; LOCKED STATES; INCOHERENT STATE; SYNCHRONIZATION; MODEL; OSCILLATORS; STABILITY; ENTRAINMENT; POPULATIONS; INSTABILITY; EMERGENCE;

D O I：

10.3934/cpaa.2021013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study phase concentration for the Kuramoto-Sakaguchi(K-S) equation with frustration via detailed estimates on the dynamics of order parameters. The Kuramoto order parameters measure the overall degree of phase concentrations. When the coupling strength is sufficiently large and the size of frustration parameter is sufficiently small, we show that the amplitude order parameter has a positive lower bound uniformly in time, and we also show that the total mass concentrates on the translated phase order parameter by a frustration parameter asymptotically, whereas the mass in the region around the antipodal point decays to zero exponentially fast.

引用

页码：2579 / 2612

页数：34

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