Influence of colored cross-correlated noise on stochastic resonance for an underdamped bistable system subjected to multiplicative and additive noises

The stochastic resonance (SR) behavior for an underdamped bistable system with colored cross-correlated noise between multiplicative and additive noise is investigated. The stationary probability density is obtained under the condition of the detailed balance. The expressions for the signal-to-noise ratios (SNRs) for two initial states is deduced by applying two-state theory under the adiabatic condition. The analysis result indicates that the SR phenomenon takes place when the SNRs vary with the coupling strength and the correlation time of the cross-correlated noise. Double SR phenomenon occurs on SNRs’ curves with the increase of the strength of the additive noise. One resonance peak exists when the SNRs change with the damping coefficient and with the intensity of the multiplicative noise.