A nonlinear stochastic delay differential system with symmetry SD oscillator is investigated to detect weak signal. Firstly, the stochastic Melnikov function and the chaos threshold are obtained by using the stochastic mean square criterion. Secondly, the stochastic center manifold and the stochastic averaging method are used to obtain the one-dimensional $It\hat{o}$ equation and the corresponding FPK equation. The stationary probability density of the FPK equation is studied and the corresponding nonlinear stochastic dynamical behaviors are analyzed. Finally, the highlight of this paper is to detect the weak signal with ‘transient vacancy in chaotic motions’ (TVICMs) method successfully and extract the features information such as frequency and amplitude on the premise of unknown features information. Astonishingly, numerical simulation shows that the time delay can enhance the detection capability of the system and the effectiveness of the new method.

研究了带有对称SD振荡器的非线性随机时滞差分系统，用于检测弱信号。首先，利用随机均方准则获得了随机梅尔尼科夫函数和混沌阈值。其次，采用随机中心流形和随机平均法求一维$\mathrm{一世}Ť\widehat{Ø}$方程和相应的FPK方程。研究了FPK方程的平稳概率密度，并分析了相应的非线性随机动力学行为。最后，本文的重点是成功地利用“混沌运动中的瞬时空位”（TVICMs）方法检测弱信号，并在未知特征信息的前提下提取频率和幅度等特征信息。令人惊讶的是，数值仿真表明，时延可以增强系统的检测能力和新方法的有效性。