The Effects of Time Delay on Stochastic Resonance in a Bistable System with Correlated Noises

The effects of time delay on stochastic resonance (SR) in a bistable system with time delay, correlated noises and periodic signal are studied by using the theory of signal-to-noise ratio (SNR). The expression of the SNR is derived under the adiabatic limit and the small delay time approximation. It is found that: (i) For the case of no correlations between multiplicative and additive noise, the delay time tau can enhance the SNR as a function of the multiplicative noise intensity alpha and it can restrain the SNR as a function of the additive noise intensity D; (ii) For the case of correlations between multiplicative and additive noise, tau can induce a minimum and maximum in curve of the SNR as a function of alpha, and can intensively restrain the SNR as a function of the D and there is a critical value of delay tim tau (c) =0.1 in the height of the SNR peak with change of tau, i.e., when tau takes value blow tau (c) , the tau boosts up the SNR as a function of the strength lambda of correlations between multiplicative and additive noise, however, when tau takes value above tau (c) , the tau restrains that.