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Noise- and delay-induced regime shifts in an ecological system of vegetation

In this paper, the stationary probability distribution (SPD) and mean first passage time (MFPT) in a vegetation model with time delay are investigated, where the vegetation dynamics is assumed to be disturbed by both intrinsic and extrinsic noises. The impacts of the intrinsic noise strength α, extrinsic noise strength D, time delay τ and cross-correlation strength q between two noises on the SPD and MFPT of the regime shifts between the sustainable vegetation and barren states are discussed, respectively. Our main results are as follows. (i) The increase of α will cause regime shifts from the barren state to the sustainable vegetation state, while the increase of D or τ will cause regime shifts from the sustainable vegetation state to the barren state. (ii) The MFPT as a function of the noise intensities (i.e., α and D) exhibits one maximum value in the case of q < 0.0, and the maximum MFPT shows the characteristic of the noise enhanced stability of the sustainable vegetation biomass. (iii) However, for the case of q ⩾ 0.0?> , the increase of α or D causes a decrease of the MFPT, i.e., the noises can enhance the probability of regime shifts to the barren state. (iv) Although the cross-correlation between two noises is positive (q > 0.0), the presence of time delay can also cause the existence of extrinsic noise enhanced stability.