Stochastic resonance in linear system due to dichotomous noise modulated by bias signal

The stochastic resonance in an over-damped linear system due to dichotomous noise modulated by a bias signal is studied in detail. By the theory of signal-to-noise ratio (SNR) and the Shapiro-Loginov formula, the exact expressions of the first two moments and SNR for the output to the asymmetric dichotomous noise input are obtained. It is found that each curve of the SNR versus the multiplicative noise intensity exhibits a mono peak and the conventional stochastic resonance appears, which is absent for the case of noise and periodic signal introduced additively. Meanwhile, the SNR is a non-monotonic function of the signal frequency or the correlation time of noise, and the bona fide stochastic resonance (SR) and SR in a broad sense exist. Moreover, the SNR depends on the additive noise intensity, cross-correlation strength and asymmetry of multiplicative noise.