With Limit Cycles Of Li¨¦nard Equations Perturbed Hopf Bifurcation

In this paper periodically perturbed Hopf bifurcation to Lienard equation with limited time delay is sdudied in detail.That is,the influence of small periodic perturbations on system exhibiting Hopf bifurcation is sdudied. In particular,the excitation frequency and the critical natural frequency of Hopf bifurcation in the cases of harmonic resonance .subharmonic resonance, ultraharmonic resonance, and ultrasubharmonic resonance is discussed.It is shown that in some parameter regions the sestyms exhibit harmonic solution bifurcation,subharmonic solution bifurcation,ultraharmonic solution bifurcation, ultrasubharmonic solution bifurcation and quasi-periodic solution. Furthermore, the stability of bifurcating periodic solutions is discussed.