Application of the method of moments for calculating the dynamic response of periodically driven nonlinear stochastic systems

It is shown that the method of moments allows one to calculate the first- and higher-harmonic susceptibilities of nonlinear stochastic systems with high accuracy. The dependence of the spectral amplification at the first three harmonics on the noise intensity is studied. It is shown that stochastic resonance at the third harmonic occurs at two separate values of the noise intensity for not too large a bias. Also, it is demonstrated that even when the bias is so large that the bistable system turns into a monostable one, the stochastic resonant enhancement of the system's sensitivity to the external driving field is still observed at some optimal non-zero value of the noise intensity.