Weak signal detection based on variable-situation-potential with time-delay feedback and colored noise

Abstract

For a long time, weak signal detection has been a research direction of great interest to scholars. This paper proposes a variable stochastic differential equation with double potential wells with time-delay feedback control, and its stochastic dynamics are studied and analyzed. Under the background of colored noise, the theoretical chaos threshold is calculated by the numerical integration method based on the Melnikov function. The influences of colored noise and time-delay feedback on the threshold are also discussed. Appropriate time-delay feedback can reduce the threshold, which is more conducive to detecting weak signals in the system. On this basis, we established a set of schemes for detecting weak signals: First, the frequency of the signal to be detected is determined by the “transient vacancy” of the system’s chaotic motion. Secondly, on the basis of the known frequency and phase of the weak signal, the amplitude of the weak signal is obtained. Finally, from the aspect of numerical simulation, this method has obvious advantages in detecting weak signals.