Stochastic resonance in bistable duffing oscillators and its dynamical
双稳杜芬振子的随机共振及其动力学机制

The method of moments is applied to the bistable Duffing oscillators driven by Gaussian white noise and weak periodic force,and the converging rate of the method is found dependent on the damping size,namely,with the same nonlinear parameter,it converges quicker if the damping coefficient is larger.Since the method of moments can make us disclose more general characteristic than only using numerical simulations,the results derived from the method of moments along with the numerical simulation results can make us to find relations between stochastic resonance and stochastic dynamical behavior.With the method of moments,the mono-peak and double-peak resonant structures in the system are disclosed with the spectral amplification factor for different drive frequencies for the case of the larger damping coefficient.To explain the derived resonant structure,the dependence of nonzero frequency peaks peaked out from fluctuating spectral density on noise intensity is investigated,and the double-peaked resonance is found to be resulted from the intrawell vibrations and the above potential barrier vibrations,which is a modification to the previous result.The study confirms there are three possible resonant sources,i.e.interwell jump,intrawell vibration and above-barrier vibration in the considered system,and the results have importance in statistical mechanics.