The influence of the periodic perturbations on Hopf bifurcation of Liénard equation with limited dlay

In this paper,the influence of small periodic perturbations on Lienard equation with limited delay exhibiting Hopf bifurcation is studied.In particular,the case where the excitation frequency is close to twice the critical natural frequency of Hopf bifurcation is discussed.The result of subharmonic solution bifurcation along with its stability is obtained.And Hopf bifurcation of the averaged system is studied.