噪声交叉关联强度的时间周期调制对线性过阻尼系统的随机共振的影响

摘要

For an over-damped linear system subjected to correlated additive and multiplicative noise and a periodic signal, when the cross-correlation intensity between noises is a time-periodic function, the analytical expression of the output signal-to-noise ratio (SNR) is derived by means of the stochastic averaging method. It is found that this system has richer dynamic behaviors than the linear systems in which cross-correlation intensity between noises is constant, that the evolution of the output SNR with the cross-correlation modulation frequency presents periodic oscillation, and that the parameters of cross-correlation intensity between noises diversify the stochastic resonance phenomena.The time-periodic modulation of cross-correlation intensity between noises is conductive to enhancing the sensitivity to weak periodic signal detection and implementing the frequency estimation of weak periodic signal.%　　针对由加性、乘性噪声和周期信号共同作用的线性过阻尼系统，在噪声交叉关联强度受到时间周期调制的情况下，利用随机平均法推导了系统响应的信噪比的解析表达式。研究发现这类系统比噪声间互不相关或噪声交叉关联强度为常数的线性系统具有更丰富的动力学特性，系统响应的信噪比随交叉关联调制频率的变化出现周期振荡型随机共振，噪声的交叉关联参数导致随机共振现象的多样化。噪声交叉关联强度的时间周期调制的引入有利于提高对微弱周期信号检测的灵敏度和实现对周期信号的频率估计。