Stochastic resonance in the logistic growth model with time-modulated correlated noise

Stochastic resonance in the logistic model driven by time-modulated correlated multiplicative and additive noises is investigated. For small amounts of the two noises, a small amplitude of the additive modulated signal and a small intensity of the time-modulated correlated noise, under the adiabatic approximation, the analysis expressions of the signal-to-noise ratios for different frequencies and equal frequencies of the two modulation forces have been obtained. Theoretical and numerical study shows that the signal-to-noise ratios vary non-monotonically with increasing intensities of the multiplicative and additive noises. The curves of the signal-to-noise ratio versus additive noise strength present two peaks while one peak exists in each of the curves for the signal-to-noise ratio as a function of the multiplicative noise intensity. In addition, for equal frequency of the two modulation forces, the signal-to-noise ratio behaves non-monotonically with increasing amplitude of the time-modulation force.