Observing nonlinear stochastic resonance with piecewise constant driving forces by the method of moments

The original method of moments confined within linear response theory is improved to calculate the nonlinear dynamic response of the standard noisy bistable stochastic systems in the general response sense by proposing a different operating technique. Especially, the proposed technique is simple and efficient to be used to the cases where the driving forces are not harmonics. Using the piecewise constant driving forces for demonstration, our comparative analysis shows that the long time ensemble average and the first three harmonic susceptibilities calculated by the proposed technique are of high accuracy. The dependence of the spectral amplification parameters at the first three harmonics on the noise intensity is also investigated, and the analysis to the resonant curves suggests a possible way to induce the even-order harmonic stochastic resonance.