Effects of colored noise on stochastic resonance in a bistable system subject to multiplicative and additive noise

Abstract

The effects of colored noise on stochastic resonance (SR) in a bistable system driven by multiplicative colored noise and additive white noise and a periodic signal are studied by using the unified colored noise approximation and the theory of signal-to-noise ratio (SNR) in the adiabatic limit. In the case of no correlations between noises, there is an optimal noise intensities ratio R at which SNR is a maximum that identifies the characteristics of the SR when the correlation time $\ensuremath{\tau}$ of the multiplicative colored noise is small. However, when $\ensuremath{\tau}$ is increased, a second optimal value of R appears, and two peaks appear in the SNR simultaneously. In the case of correlations between noises, the SNR is not only dependent on the correlation time $\ensuremath{\tau},$ but also on the intensity of correlations between noises. Moreover, the double peak phenomenon can also appear as $\ensuremath{\tau}$ is increased in certain situations.