Stochastic Resonance Of Second-order Linear System Subject To Signal With Dichotomous Noise

When a nonlinear system is driven by a random force (noise), the response of a system to the input is enhanced. This is called stochastic resonance. In past several years, stochastic resonance receives the widespread attention, and was discovered in many domains. Along with deep research, it also has found that SR exists in linear system. Stochastic resonance theory can be used to detect weak signal, and extract information from strong noise environment.This article mainly discusses two aspects of SR in the linear system. On one hand, when the system damping ratio and the system intrinsic frequency are oscillated by a stochastic telegram noise as well as the frequency of the driving signal is modulated with the some telegram noise. Based on the linear system theory and the correlation theory, the explicit expression of the output amplitude gain(OAG) of the system is obtained. It is shown that the OAG is a non-monotonic function of the system damping ratio, the system intrinsic frequency, the correlation rate of the stochastic telegram noise and the driving signal frequency. It shows that SR exits. On other hand, this paper investigates SR of an over-damped second-order linear system, where the damping ratio and the driving signal is perturbed by the dichotomous noise, as well as the system intrinsic frequency is perturbed by the other dichotomous noise. Based on the linear system theory and the correlation theory, the explicit expression of the output amplitude gain (OAG) of the system is obtained. OAG is a non-monotonic function of the system parameters. By choosing appropriate of the system and the noise, OAG can be maximized, stochastic resonance occurs.