Effects of noise on the frequency response of the monostable Duffing oscillator

The influence of noise on the frequency response of the monostable, hardening Duffing oscillator is studied. These changes are studied via the averaged dynamics (using Euler-Maruyama simulations) as well as experiments. It is found that for intermediate noise amplitudes, the qualitative shape of the frequency response curve is changed. For large noise amplitudes, the upper and lower branches of the hysteresis curve collapse into one curve. These results could be of practical significance, if an oscillator is desired to be placed on the upper or lower branch of the hysteresis curve.