Phase shifts in driven stochastic nonlinear systems

The dynamics of bistable stochastic systems driven by oscillating fields is analyzed by numerically solving the Fokker-Planck equation. The long time response is oscillatory in time and out of phase with respect to the field. The phase shift as a function of the noise D has a peak for weak fields and low frequencies if intrawell fluctuations are considered, in agreement with linear response theory. The amplitude has a peak, but for a different value of D, even if intrawell fluctuations are neglected. We also analyze the behavior for strong fields so that linear response theory becomes questionable.