Stochastic resonance in a time-delayed logistic system

The logistic system driven by noises is usually used to analyze the growth of tumor cell population. In this paper we investigated the phenomenon of stochastic resonance (SR) in the time delayed logistic system driven by correlated Gaussian white noises. The expression of the quasi-steady-state probability distribution function is obtained by the small delay approximation, and the explicit expression of the signal-to-noise ratio (SNR) of the system is derived in the adiabatic limit. The effects of the multiplicative noise intensity D, additive noise intensity Q, correlation strength λ, and delay time τ on the SNR are discussed. It is found that the curves of the SNR has a single peak with the increase of multiplicative noise intensity D and additive noise intensity Q, respectively, which means that SR appears, and the increase of the delay time τ can induce and enhance the SR.