含噪双稳杜芬振子矩方程的分岔与随机共振

研究了含噪声的双稳杜芬振子矩方程的分岔与随机共振的关系，并根据它们的关系, 从另 一个角度揭示了随机共振发生的机制. 首先在It?方程的基础上，导出了双稳杜芬振子在白噪声和弱周期信号作用下的矩方程，其次以噪声强度 为分岔参数分析了矩方程的分岔特性，再次分析了矩方程的分岔与双稳杜芬振子随机共振 之间的关系，最后根据该对应关系从另一种观点提出了双稳杜芬振子随机共振的机制，该 机制是由于以噪声强度为分岔参数的矩方程发生了分岔，而分岔使得原系统响应均值的能量分布发生了转移，使能 量向频率等于输入信号频率的分量处集中，使得弱信号得到了放大，随机共振发生了.

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

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.