The Periodically Perturbed Hopf Bifurcation For Price Reyleigh Equation With Delay

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