Using delay to quench undesirable vibrations

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