Using delay to quench undesirable vibrations

A van der Pol type system with delayed feedback is explored by employing the two variable expansion perturbation method. The perturbation scheme is based on choosing a critical value for the delay corresponding to a Hopf bifurcation in the unperturbed epsilon=0 system. The resulting amplitude-delay relation predicts two Hopf bifurcation curves, such that in the region between these two curves oscillations will be quenched. The perturbation results are verified by comparison with numerical integration.