The Impact Of The Time Delay In The Vegetation Ecological System Under Stochastic Perturbations

Because of the human activities, the vegetation ecosystem has degenerated seriously. The degradation of vegetation tends to cause a decline in biological diversity, the destruction of the ecological balance, climate deterioration, etc., which threatens seriously the safety of human life and property. So far, re-searchers have considered the white noise and investigated the impacts of the intrinsic noise and the extrinsic noise on the vegetation ecological system. This thesis uses theoretical analysis combining with numerical simulation and inves-tigates the impacts of the white noise combining with the time delay(T) and the colored noise on the dynamic behavior of vegetation ecological system.In this paper, we investigate the impacts of the wite noises combining with T on the stationary probability distribution (SPD), mean first passage time(MFPT) and stochastic resonance phenomena(SR) of vegetation ecological system. Research results show that:(1) The intrinsic noise(a) and negative cross-correlation between two noises can induce regime shifts from the barren state to the sustainable vegetation one. However, the extrinsic noise(D), T and positive cross-correlation can induce regime shifts to the barren one. (2) When k< 0.0, the noises can enhance the stability of the ecological system. However, when k≥0.0, the noises weaken the stability of the system. While under the effect of T, D enhances the stability of the system. (3) When the signal-to-noise ratio(SNR) as a function of α, t or k enhances SR and the stochastic reverse-resonance phenomenon, while SNR as a function of D, T or k weakens SR, and SNR as a function of k, T not only can enhance SNR but also can lead to double resonance phenomenon of the ecological system.Secondly, we investigate the impacts of colored noises on the SPD, MFPT, SR of the vegetation ecological ecosystem. Research results show that:(1) The self-correlation time of the extrinsic noise(T1) can induce regime shifts from the desert state to the sustainable vegetation state. However, the self-correlation time of the intrinsic noise(T2), the cross-correlation time(r3) and strength(k) can induce regime shifts to the desert state. (2) T1 or T2 can enhance the stability of the sustainable vegetatio, while T3 or k weakens the stability of the sustainable vegetation. (3) When SNR as a function of a, T1 or T2 enhances SR of the system while T3 weakens SR, when SNR as a function of D and D is smaller, T3 enhances the stochastic reverse-resonance phenomenon, T1 or T2 weakens the stochastic reverse-resonance phenomenon and emerges of stochastic reverse-resonance platform, when SNR as a function of D and D becomes larger, T2 enhances SR. As increasing of T2 or T3, SR is weakened then enhanced. When SNR as a function of k, T2 or T3 enhances SR, T1 weakens SR then enhances SR.