Complete synchronization of Kuramoto oscillators with finite inertia

被引：109

作者：

Choi, Young-Pit ^{[1
]}

Ha, Seung-Yeal ^{[1
]}

Yun, Seok-Bae ^{[2
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2011年 / 240卷 / 01期

关键词：

Kuramoto model; Inertia effects; Phase; Frequency; Complete synchronization; COUPLED OSCILLATORS; MODEL; POPULATIONS; STABILITY; ARRAYS;

D O I：

10.1016/j.physd.2010.08.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an approach based on Gronwall's inequalities for the asymptotic complete phase-frequency synchronization of Kuramoto oscillators with finite inertia. For given finite inertia and coupling strength, we present admissible classes of initial configurations and natural frequency distributions, which lead to the complete phase-frequency synchronization asymptotically. For this, we explicitly identify invariant regions for the Kuramoto flow, and derive second-order Gronwall's inequalities for the evolution of phase and frequency diameters. Our detailed time-decay estimates for phase and frequency diameters are independent of the number of oscillators. We also compare our analytical results with numerical simulations. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：32 / 44

页数：13

共 27 条

[1] The Kuramoto model:: A simple paradigm for synchronization phenomena [J].

Acebrón, JA ;

Bonilla, LL ;

Vicente, CJP ;

Ritort, F ;

Spigler, R .

REVIEWS OF MODERN PHYSICS, 2005, 77 (01) :137-185

[2] Synchronization in populations of globally coupled oscillators with inertial effects [J].

Acebrón, JA ;

Bonilla, LL ;

Spigler, R .

PHYSICAL REVIEW E, 2000, 62 (03) :3437-3454

[3] Adaptive frequency model for phase-frequency synchronization in large populations of globally coupled nonlinear oscillators [J].

Acebron, JA ;

Spigler, R .

PHYSICAL REVIEW LETTERS, 1998, 81 (11) :2229-2232

[4] STUDY OF LOCKING PHENOMENA IN OSCILLATORS [J].

ADLER, R .

PROCEEDINGS OF THE IEEE, 1973, 61 (10) :1380-1385

[5] BIOLOGY OF SYNCHRONOUS FLASHING OF FIREFLIES [J].

BUCK, J ;

BUCK, E .

NATURE, 1966, 211 (5049) :562-&

[6] Synchronization of coupled rotators: Josephson junction ladders and the locally coupled Kuramoto model [J].

Daniels, BC ;

Dissanayake, STM ;

Trees, BR .

PHYSICAL REVIEW E, 2003, 67 (02) :14

[7] AN ADAPTIVE MODEL FOR SYNCHRONY IN THE FIREFLY PTEROPTYX-MALACCAE [J].

ERMENTROUT, B .

JOURNAL OF MATHEMATICAL BIOLOGY, 1991, 29 (06) :571-585

[8] On the complete synchronization of the Kuramoto phase model [J].

Ha, Seung-Yeal ;

Ha, Taeyoung ;

Kim, Jong-Ho .

PHYSICA D-NONLINEAR PHENOMENA, 2010, 239 (17) :1692-1700

[9] Spontaneous phase oscillation induced by inertia and time delay [J].

Hong, H ;

Jeon, GS ;

Choi, MY .

PHYSICAL REVIEW E, 2002, 65 (02)

[10] Inertia effects on periodic synchronization in a system of coupled oscillators [J].

Hong, H ;

Choi, MY ;

Yi, J ;

Soh, KS .

PHYSICAL REVIEW E, 1999, 59 (01) :353-363

← 1 2 3 →