The Dynamics of Two Coupled van der Pol Oscillators with Delay Coupling

We investigate the dynamics of a system of twovan der Pol oscillators with delayed velocity coupling.We use the method of averaging to reduce the problem to the studyof a slow-flow in three dimensions.We study the steady state solutions of this slow-flow, with specialattention given to the bifurcations accompanying their change innumber and stability. We compare these stability results with numericalintegration of the original equations and show that the two sets of resultsare in excellent agreement under certain parameter restrictions.Our interest in this system is due to its relevance to coupled laseroscillators.