Bifurcations in the dynamics of two coupled Van Der Pol Oscillators with delay coupling

Stephen Wirkus; Richard Rand

doi:10.1115/DETC99-VIB-8318

Bifurcations in the dynamics of two coupled Van Der Pol Oscillators with delay coupling

Stephen Wirkus, Richard Rand

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

2 Scopus citations

Abstract

We investigate the dynamics of a system of two van der Pol oscillators with delayed velocity coupling. We use the method of averaging to reduce the problem to the study of a slow-flow in three dimensions. We study the steady state solutions of this slow flow, with special attention given to the bifurcations accompanying their change in number and stability. Our interest in this system is due to its relevance to coupled laser oscillators.

Original language	English (US)
Title of host publication	17th Biennial Conference on Mechanical Vibration and Noise
Publisher	American Society of Mechanical Engineers (ASME)
Pages	2559-2568
Number of pages	10
ISBN (Electronic)	9780791880395
DOIs	https://doi.org/10.1115/DETC99-VIB-8318
State	Published - 1999
Externally published	Yes
Event	ASME 1999 Design Engineering Technical Conferences, DETC 1999 - Las Vegas, United States Duration: Sep 12 1999 → Sep 16 1999

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	7B-1999

Conference

Conference	ASME 1999 Design Engineering Technical Conferences, DETC 1999
Country/Territory	United States
City	Las Vegas
Period	9/12/99 → 9/16/99

ASJC Scopus subject areas

Mechanical Engineering
Computer Graphics and Computer-Aided Design
Computer Science Applications
Modeling and Simulation

Access to Document

10.1115/DETC99-VIB-8318

Cite this

Bifurcations in the dynamics of two coupled Van Der Pol Oscillators with delay coupling. / Wirkus, Stephen; Rand, Richard.
17th Biennial Conference on Mechanical Vibration and Noise. American Society of Mechanical Engineers (ASME), 1999. p. 2559-2568 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 7B-1999).

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

Wirkus, S & Rand, R 1999, Bifurcations in the dynamics of two coupled Van Der Pol Oscillators with delay coupling. in 17th Biennial Conference on Mechanical Vibration and Noise. Proceedings of the ASME Design Engineering Technical Conference, vol. 7B-1999, American Society of Mechanical Engineers (ASME), pp. 2559-2568, ASME 1999 Design Engineering Technical Conferences, DETC 1999, Las Vegas, United States, 9/12/99. https://doi.org/10.1115/DETC99-VIB-8318

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abstract = "We investigate the dynamics of a system of two van der Pol oscillators with delayed velocity coupling. We use the method of averaging to reduce the problem to the study of a slow-flow in three dimensions. We study the steady state solutions of this slow flow, with special attention given to the bifurcations accompanying their change in number and stability. Our interest in this system is due to its relevance to coupled laser oscillators.",

author = "Stephen Wirkus and Richard Rand",

note = "Funding Information: The authors wish to thank Professor Rick Compton for proposing this problem, and Professor Steven Strogatz for helpful suggestions. Publisher Copyright: {\textcopyright} 1999 by ASME; ASME 1999 Design Engineering Technical Conferences, DETC 1999 ; Conference date: 12-09-1999 Through 16-09-1999",

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AB - We investigate the dynamics of a system of two van der Pol oscillators with delayed velocity coupling. We use the method of averaging to reduce the problem to the study of a slow-flow in three dimensions. We study the steady state solutions of this slow flow, with special attention given to the bifurcations accompanying their change in number and stability. Our interest in this system is due to its relevance to coupled laser oscillators.

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Bifurcations in the dynamics of two coupled Van Der Pol Oscillators with delay coupling

Abstract

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Conference

ASJC Scopus subject areas

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