The bifurcation of noisy bistable Duffing oscillator's moment equations and stochastic resonance

In this paper, the relationship between thebifurcation of noisy bistable Duffing oscillator's moment equations andstochastic resonance of this system is studied. According to therelationship, the mechanism of stochastic resonance of the bistable Duffingoscillator is revealed from another viewpoint. First, the momentequations of the bistable Duffing oscillator in the presence of Gaussiandistributed white noise and weak periodic signal are obtained on the basisof It\hat\rm o equation. Second, the bifurcation behavior of its momentequations with noise intensity as their bifurcation parameter is analyzed.Third, the relationship between stochastic resonance of the bistable Duffingoscillator and the behavior of bifurcation of the moment equations is studiedquantitatively. Finally, the mechanism ofstochastic resonance of the bistable Duffing oscillator is presented fromanother viewpoint, that is, the transfer of the energy distribution of thefirst moment of the original system response occurs because of occurrence ofbifurcation of the moment equations with noise intensity bifurcation parameter,and the transfer makes the energy of system response concentrate in thefrequency component whose frequency is equal to that of input, then the weaksignal is amplified and stochastic resonance occurs.