乘性噪声作用下线性模型中的随机共振

Stochastic Resonance of a Linear Model Subject under Multiplicative Noise

随机共振是指在一定噪声强度和外部激励的共同作用下,动力学系统的输出响应达到最大值的一种非线性现象。本文研究了乘性噪声作用下线性模型的随机共振现象。根据噪声的特性和线性系统理论,得到了系统输出幅度增益的精确表达式。研究发现,输出幅度增益是激励信号频率以及系统参数的非单调函数,即出现了随机共振现象。输出幅度增益随噪声强度、自相关率的增大而单调地增大。选择适当的参数,系统输出幅度增益可以大于1,即有噪声时的系统输出平均幅度可以大于无噪声时的输出幅度增益。该结果对于微弱信号检测有一定的意义,对于传统的线性系统理论是一个有益的补充。

Stochastic resonance is a nonlinear effect that accounts for the optimum response of a dynamical system in an external stimulation at certain noise intensity. In this paper, the phenomenon of stochastic resonance in a linear model subject under multiplicative noise is investigated. By applying the noise character and the linear system theory, the explicit expression of the output amplitude gain （OAG） of the linear system is obtained. It is shown that the OAG is a non-monotonic function of the frequency of the stimulating signal and of the parameters of the system, i.e. , the stochastic resonance phenomenon occurs. In addition, the OAG increases monotonically with the increase of the noise strength and the noise correlation rate. By choosing appropriate parameters of the noise and the system, the OAG of the system can be larger than one, i. e. , the OAG of the noisy system can be larger than that of the noise free system. The result is of certain significance in weak signal detection, and provides a good supplement to conventional linear system theory.