Impact of Double Time Delays on Regime Shift and Stochastic Resonance for a Species Population System Driven by Colored Correlated Multiplicative and Additive Noises

Abstract

In this paper, the characteristics for the state transition between the boom state and the extinction one, varius stochastic resonance (SR) phenomena for a species population system induced by double time delays and colored cross-correlated Gaussian noises are investigated. The control of the species population system has an important effect on ecological balance and the development of human living environment. By means of the numerical calculation of the mean extinction time and the stationary probability density function (SPDF), we can figure out some fact: both external and internal noises, the noise correlation strength and its correlation time, one time delay can all reduce the ecological stability and shorten the survival time of the system; while the other time delay can enhance significantly the biological stability and postpone the extinction of the population. For the mean extinction time (MET) of the species population, it is found that noise correlation strength, time delay, the noise correlation time can all reduce the peak value of the MET, which leads to the reduction of the life cycle. Inversely, the other time delay will not change the maximum of the MET, and induce the peak value to shift to the left. With respect to the SNR, it is discovered that in the noise correlation strength and its correlation time, one-time delay mainly plays a prominent role in inhibiting the SR effect. On the contrary, the multiplicative noise can result in the enhancement of the resonant peak. In particular, the other time delay and the additive noise can stimulate the SR effect for the SNR during the initial period. However, the further increase of them will bring about the reduction of the resonant phenomenon.