Effects of time-periodic modulation of cross-correlation intensity between noises on stochastic resonance of over-damped linear system

For an over-damped linear system subjected to correlated additive and multiplicative noise and a periodic signal, when the cross-correlation intensity between noises is a time-periodic function, the analytical expression of the output signal-to-noise ratio (SNR) is derived by means of the stochastic averaging method. It is found that this system has richer dynamic behaviors than the linear systems in which cross-correlation intensity between noises is constant, that the evolution of the output SNR with the cross-correlation modulation frequency presents periodic oscillation, and that the parameters of cross-correlation intensity between noises diversify the stochastic resonance phenomena. The time-periodic modulation of cross-correlation intensity between noises is conductive to enhancing the sensitivity to weak periodic signal detection and implementing the frequency estimation of weak periodic signal.