Effects of forcing frequency on dynamics of subcritical hopf bifurcation under periodic perturbation

In this paper, we analyze effects of frequency of periodic perturbation on a nonlinear system with subcritical hopf bifurcation, and find that the relationship between system dynamics and perturbation frequency is complexity. Forcing frequency affects transitions, such as bifurcation and hysteresis, in diagram of periodic solution amplitude (with the same frequency as forcing frequency) versus bifurcation parameter. Forcing frequency also has influence on system stability boundary. Under certain condition, system has worst stability performance when forced by periodic perturbation with hopf frequency. The results gotten in general nonlinear system are applied into rotating stall of axial compressor.