Stochastic Resonance Of Linear System Driven By Dichotomic Noise

In general, stochastic resonance (SR) occurs when an output signal is a non-monotonic function of the parameters of noise or periodic signal in a system with noise. The signal-to-noise rate (SNR), the output amplitude gain (OAG) are always used to study SR, because their the non-monotonic dependence of the noise parameters and system parameters. Therefore, more and more researchers are interested in the SNR and OAG of a first-order system and a second-order system with noise.This article mainly discusses two aspects of SR. on one hand, SR has been investigated in the first-order linear system, where driven by Gaussian multiplicative noise or Poissonian multiplicative noise, but the additive noise is ignored. SR did not occur when the first-order linear system only driven by an additive Gaussian white noise. We investigate SR in the first-order linear system driven by additive and multiplicative dichotomous noise. Numerical results show that SR occurs when the noise correlation coefficientλ＜0. On the other hand, SR occurs in a second-order linear system, where the inductance and the system intrinsic frequency driven by a dichotomous noise. However, SR hasn't been studied in a second-order linear system, where two different system parameters are driven by two dichotomous noises. We have found that SR occurs in an over-damped second-order system, where the system damping coefficient is driven by the dichotomous noise, and the frequency of the driving signal is perturbed by the another dichotomous noise. Based on linear system theory and the theory of signal and system, the explicit expression of the OAG of the system is obtained. The OAG is a non-monotonic function of the system intrinsic frequency, the system damping coefficient, the frequency of the driving signal, the correlation rate of the dichotomous noise, and the coupling intensity between the two noises. Numerical results show that the SR occurs when the system parameters and noise parameters change. Furthermore, by choosing appropriate parameters of the dichotomous noise and the system, the OAG of the noisy system can be larger than that of the noise-free system.