Influence of noise on frequency responses of softening Duffing oscillators

In the present study, the influence of noise on the responses of continuous-time dynamical systems are considered. In particular, the influence of white Gaussian noise on the frequency responses of monostable and bistable, softening Duffing oscillators are studied. A combination of experimental, analytical, and numerical studies are undertaken to understand the shifting of jump-up and jump-down frequencies and an eventual collapse of upper and lower responses branches of into one response curve with no jump instabilities for the considered Duffing oscillator. It is noted that with noise, the hysteresis observed in the response of the nonlinear oscillator without noise can be destroyed.