The dynamics of two coupled van der Pol oscillators with delay coupling

Stephen Wirkus, Richard Rand

Research output: Contribution to journalArticle

121 Citations (Scopus)

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. We compare these stability results with numerical integration of the original equations and show that the two sets of results are in excellent agreement under certain parameter restrictions. Our interest in this system is due to its relevance to coupled laser oscillators.

Original languageEnglish (US)
Pages (from-to)205-221
Number of pages17
JournalNonlinear Dynamics
Volume30
Issue number3
DOIs
StatePublished - Nov 2002
Externally publishedYes

Fingerprint

Van Der Pol Oscillator
Coupled Oscillators
Steady-state Solution
Numerical integration
Averaging
Three-dimension
Bifurcation
Laser
Restriction
Lasers
Relevance

Keywords

  • Bifurcations
  • Coupled oscillators
  • Differential-delay equations
  • Phase-locking

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Computational Mechanics

Cite this

The dynamics of two coupled van der Pol oscillators with delay coupling. / Wirkus, Stephen; Rand, Richard.

In: Nonlinear Dynamics, Vol. 30, No. 3, 11.2002, p. 205-221.

Research output: Contribution to journalArticle

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