Dynamics of an oscillator with delay parametric excitation

摘要: This paper involves the dynamics of a delay limit cycle oscillator being driven by time-varying perturbation in delay: x=−x(t−T(t))−ϵx3 with T(t)=π2+ϵk+ϵcosωt. is chosen to periodically cross stability boundary for x=0 equilibrium constant-delay system. For most parameter space, system non-resonant, leading quasiperiodic behavior. However, region 2:1 resonance shown exist where system׳s response frequency entrained half forcing ω. By combination analytical and numerical methods, we find that transition between behavior consists variety local global bifurcations, with corresponding regions multiple stable unstable steady-states.