The spectrum of the locked state for the Kuramoto model of coupled oscillators

被引：166

作者：

Mirollo, RE

Strogatz, SH

机构：

[1] Boston Coll, Dept Math, Chestnut Hill, MA 02467 USA

[2] Cornell Univ, Ctr Appl Math, Ithaca, NY 14853 USA

[3] Cornell Univ, Dept Theoret & Appl Mech, Ithaca, NY 14853 USA

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2005年 / 205卷 / 1-4期

基金：

美国国家科学基金会;

关键词：

synchronization; coupled oscillators; phase-locking; Kuramoto model;

D O I：

10.1016/j.physd.2005.01.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the linear stability of the phase-locked state in the Kuramoto model of coupled oscillators. The main result is the first rigorous characterization of the spectrum and its associated eigenvectors, for any finite number of oscillators. All but two of the eigenvalues are negative, and merge into a continuous spectrum as the number of oscillators tends to infinity. One eigenvalue is always zero, by rotational invariance. The final eigenvalue, corresponding to a collective mode, determines the stability of the locked state. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：249 / 266

页数：18

共 6 条

[1]

ERMENTROUT GB, 1985, J MATH BIOL, V22, P1

[2] STATISTICAL MACRODYNAMICS OF LARGE DYNAMICAL-SYSTEMS - CASE OF A PHASE-TRANSITION IN OSCILLATOR COMMUNITIES [J].

KURAMOTO, Y ;

NISHIKAWA, I .

JOURNAL OF STATISTICAL PHYSICS, 1987, 49 (3-4) :569-605

[3]

Kuramoto Yoshiki, 1975, LECT NOTE PHYS, V39, P420, DOI DOI 10.1007/BFB0013365

[4] From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators [J].

Strogatz, SH .

PHYSICA D, 2000, 143 (1-4) :1-20

[5] LYAPUNOV FUNCTION FOR THE KURAMOTO MODEL OF NONLINEARLY COUPLED OSCILLATORS [J].

VANHEMMEN, JL ;

WRESZINSKI, WF .

JOURNAL OF STATISTICAL PHYSICS, 1993, 72 (1-2) :145-166

[6] BIOLOGICAL RHYTHMS AND BEHAVIOR OF POPULATIONS OF COUPLED OSCILLATORS [J].

WINFREE, AT .

JOURNAL OF THEORETICAL BIOLOGY, 1967, 16 (01) :15-&

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