Periodically Perturbed Hopf Bifurcation For Van Der Pol-Duffing Time-delay System

This paper discusses which has the cubic term Van der Pol- Duffing non-linear time-delay system stability and the Hopf bifurcation, and has analyzed when the system experiences the Hopf bifurcation , the influence of small periodical perturbation to the system, by constructing center manifold and the method of integral average discusses the case when the perturbation frequency and the critical natural frequency of Hopf bifurcation harmonic resonance (subharmonic resonance,ultraharmonic resonance and ultrasubhar-monic resonance), It is shown that in some parameter region, the system exists harmonic solution bifurcation (subharmonic solution bifurcation, ultraharmonic solution bifurcation ,ultrasubharmonic solution bifurcation), Furthermore ,the stability of bifurcating periodic solution and the role of time-delay are discussed .