Stochastic resonance for a bistable system with multiplicative noise and additive recycled noise

The stochastic resonance (SR) phenomenon for a bistable system with multiplicative noise and additive recycled noise is investigated. The transition rate caused by the master noise and that by the recycled noise have been obtained. The spectral amplification (SA) for the system has been derived. It is shown that the SR phenomenon appears when the SA varies with the feed coefficient of the recycled noise. Periodic SR behavior can be observed when the SA changes with the increase in the time delay of the recycled noise. The SA displays a resonance peak at certain level of the multiplicative and additive noise, displaying the signature of SR. The non-monotonous influence of the system parameters on the SA is also discussed.