Effect of Time Delay and Cross-Correlated Noises on Stochastic Resonance for a Metapopulation System with a Multiplicative Periodic Signal

Abstract

In this paper, stochastic resonance (SR) in a time-delayed metapopulation system subjected to cross-correlated noises and a multiplicative signal is investigated. By using the fast descent method and the two-state theory, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results show that the conventional SR phenomenon appears in the metapopulation model under different values of the system parameters. The results demonstrate that the strength of the correlation noise λ always plays a decisive role in motivating the SR phenomenon. On the other hand, for the case of λ ＞ 0, the intensities of the multiplicative and additive noises and the time delay can all weaken the effect of SR; for the case of λ ＜ 0, the multiplicative noise can restrain the effect of SR, the weak additive noise can excite the effect of SR, the time delay τ can produce different effects on the SNR under the conditions of different parameters.