The TVICMs method for weak signal detection based on a nonlinear stochastic delay differential system

Abstract

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 Itoˆ 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.