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

Stephen Wirkus, Richard Rand

Research output: Contribution to journalArticlepeer-review

151 Scopus citations


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
Issue number3
StatePublished - Nov 2002
Externally publishedYes


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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering


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