Stochastic resonance in a bistable system subject to multiplicative and additive noise

The stochastic resonance (SR) phenomenon in a bistable system under the sim ultaneous action of multiplicative and additive noise and periodic signal i s studied by using the theory of signal-to-noise ratio (SNR) in the adiabat ic limit. Two cases have been considered: the case of no correlations betwe en multiplicative and additive noise and the case of correlations between t wo noises. The expressions of the SNR for both cases are obtained. The effe cts of intensity of multiplicative and additive noise and the intensity of the correlations between noises on the SNR are discussed for both cases, re spectively. It is found that the existence of a maximum in the SNR is the i dentifying characteristic of the SR phenomenon. In the case of no correlati ons between multiplicative and additive noise; the SNR is independent of th e initial condition of the system. However, the SNR is not only dependent o n the intensity of correlations between noises, but also on the initial con dition of the system in the presence of correlations between two noises.