Stability analysis on Kuramoto model of coupled oscillators

Wenxue Wang; Bijoy Ghosh

doi:10.3182/20080706-5-KR-1001.3669

Stability analysis on Kuramoto model of coupled oscillators

Wenxue Wang, Bijoy Ghosh

Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

In this paper we study the problem of stability for one of the most popular models of coupled phase oscillators, the Kuramoto model. The Kuramoto model is used to describe the phenomenon of collective synchronization, in which an enormous system of oscillators spontaneously locks to a common frequency although the oscillators have distinct natural frequencies. In the paper we consider the stability of the Kuramoto model of coupled oscillators with identical natural frequency and provide a stability analysis of phase difference equilibrium. The stability of the phase difference equilibrium make it possible to apply the Kuramoto model in pattern recognition.

Original language	English
Title of host publication	Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC
Edition	1 PART 1
DOIs	https://doi.org/10.3182/20080706-5-KR-1001.3669
State	Published - 2008
Event	17th World Congress, International Federation of Automatic Control, IFAC - Seoul, Korea, Republic of Duration: Jul 6 2008 → Jul 11 2008

Publication series

Name	IFAC Proceedings Volumes (IFAC-PapersOnline)
Number	1 PART 1
Volume	17
ISSN (Print)	1474-6670

Conference

Conference	17th World Congress, International Federation of Automatic Control, IFAC
Country/Territory	Korea, Republic of
City	Seoul
Period	07/6/08 → 07/11/08

Keywords

Nonlinear systems

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10.3182/20080706-5-KR-1001.3669

Cite this

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title = "Stability analysis on Kuramoto model of coupled oscillators",

abstract = "In this paper we study the problem of stability for one of the most popular models of coupled phase oscillators, the Kuramoto model. The Kuramoto model is used to describe the phenomenon of collective synchronization, in which an enormous system of oscillators spontaneously locks to a common frequency although the oscillators have distinct natural frequencies. In the paper we consider the stability of the Kuramoto model of coupled oscillators with identical natural frequency and provide a stability analysis of phase difference equilibrium. The stability of the phase difference equilibrium make it possible to apply the Kuramoto model in pattern recognition.",

keywords = "Nonlinear systems",

author = "Wenxue Wang and Bijoy Ghosh",

note = "Funding Information: ⋆ Research was partially supported from NSF grants ECS−9976174, and ECS− 0323693.; 17th World Congress, International Federation of Automatic Control, IFAC ; Conference date: 06-07-2008 Through 11-07-2008",

year = "2008",

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language = "English",

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Wang, W & Ghosh, B 2008, Stability analysis on Kuramoto model of coupled oscillators. in Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC. 1 PART 1 edn, IFAC Proceedings Volumes (IFAC-PapersOnline), no. 1 PART 1, vol. 17, 17th World Congress, International Federation of Automatic Control, IFAC, Seoul, Korea, Republic of, 07/6/08. https://doi.org/10.3182/20080706-5-KR-1001.3669

Stability analysis on Kuramoto model of coupled oscillators. / Wang, Wenxue; Ghosh, Bijoy.
Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC. 1 PART 1. ed. 2008. (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 17, No. 1 PART 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Stability analysis on Kuramoto model of coupled oscillators

AU - Wang, Wenxue

AU - Ghosh, Bijoy

N1 - Funding Information: ⋆ Research was partially supported from NSF grants ECS−9976174, and ECS− 0323693.

PY - 2008

Y1 - 2008

N2 - In this paper we study the problem of stability for one of the most popular models of coupled phase oscillators, the Kuramoto model. The Kuramoto model is used to describe the phenomenon of collective synchronization, in which an enormous system of oscillators spontaneously locks to a common frequency although the oscillators have distinct natural frequencies. In the paper we consider the stability of the Kuramoto model of coupled oscillators with identical natural frequency and provide a stability analysis of phase difference equilibrium. The stability of the phase difference equilibrium make it possible to apply the Kuramoto model in pattern recognition.

AB - In this paper we study the problem of stability for one of the most popular models of coupled phase oscillators, the Kuramoto model. The Kuramoto model is used to describe the phenomenon of collective synchronization, in which an enormous system of oscillators spontaneously locks to a common frequency although the oscillators have distinct natural frequencies. In the paper we consider the stability of the Kuramoto model of coupled oscillators with identical natural frequency and provide a stability analysis of phase difference equilibrium. The stability of the phase difference equilibrium make it possible to apply the Kuramoto model in pattern recognition.

KW - Nonlinear systems

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M3 - Conference contribution

AN - SCOPUS:79961018943

SN - 9783902661005

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

BT - Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC

T2 - 17th World Congress, International Federation of Automatic Control, IFAC

Y2 - 6 July 2008 through 11 July 2008

ER -

Stability analysis on Kuramoto model of coupled oscillators

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