The bifurcation of noisy bistable Duffing oscillator''s moment equations and stochastic resonance
含噪双稳杜芬振子矩方程的分岔与随机共振

In this paper,the relationship between the bifurcation of noisy bistable Duffing oscillator's moment equations and stochastic resonance of this system is studied.According to the relationship, the mechanism of stochastic resonance of the bistable Duffing oscillator is revealed from another viewpoint. First, the moment equations of the bistable Duffing oscillator in the presence of Gaussian distributed white noise and weak periodic signal are obtained on the basis of Ito equation.Second,the bifurcation behavior of its moment equations with noise intensity as their bifurcation parameter is analyzed.Third,the relationship between stochastic resonance of the bistable Duffing oscillator and the behavior of bifurcation of the moment equations is studied quantitatively. Finally,the mechanism of stochastic resonance of the bistable Duffing oscillator is presented from another viewpoint, that is, the transfer of the energy distribution of the first moment of the original system response occurs because of occurrence of bifurcation of the moment equations with noise intensity bifurcation parameter, and the transfer makes the energy of system response concentrate in the frequency component whose frequency is equal to that of input, then the weak signal is amplified and stochastic resonance occurs.