Study on resonance and bifurcation of fractional order nonlinear Duffing System

In this paper, resonance and bifurcation of a nonlinear damped fractional-order Duffing system are studied. The amplitude and phase of the steady-state response of system are obtained by means of average method, and then the amplitude-frequency characteristic curves of the system under different parameters are drawn based on the implicit function equation of amplitude. Grunwald-Letnikov fractional derivative is used to discretize the system numerically, and the response curve and phase trajectory of the system under different parameters are obtained, and the dynamic behavior is analyzed. The forked bifurcation behavior and saddle bifurcation behavior of the system under different parameters are investigated by numerical simulation.