Noises-induced regime shifts and -enhanced stability under a model of lake approaching eutrophication

In this paper, we study the lake eutrophication by using a stochastic model that includes both input noise and recycling noise. The effects of the input noise (α), the recycling noise (D) and the cross-correlation between two noises (λ) in the model are discussed, respectively. Our results show: (i) the noise-induced ecological bistability (EB) expands in comparison with the deterministic case; (ii) noises still can induce EB when the recycling parameter r < 0.5; (iii) the noises can cause the regime shifts from the eutrophic state to the oligotrophic one (noise-induced oligotrophy); and (iv) the input noise can accelerate regime shifts from the oligotrophic state to the eutrophic one for the case of zero or small cross-correlation. Moreover, for the case of higher cross-correlation intensity, the mean first passage time (MFPT) as a function of α exhibits a maximum, which identifies the input noise-enhanced stability (NES) of the oligotrophic state. Finally, for whatever value of cross-correlation intensity, the theoretical results show that the recycling noise can accelerate regime shifts from the oligotrophic state to the eutrophic one.