Colored Correlated Noises Induced Regime Shifts in a Time-delayed Lake Eutrophication Ecosystem

The catastrophic regime shifts in the lake eutrophication ecosystems may be usually caused by environmental perturbations, and the lake dynamics exhibit bistability characteristics with oligotrophic and eutrophic states. This paper is devoted to investigate the time delay effect in a time-delayed lake eutrophication ecosystem (TD-LEE), where the dynamics ecosystem is deemed to be disturbed by both multiplicative and additive noises. On the basis of small delay approximation, we derive the expression of the generalized effective potential function in the TD-LEE and discuss the impact of stochastic delay on the regime shifts between oligotrophic and eutrophic states. In the view of dynamical behaviors on the TD-LEE model, we also revealed that the combination with time delay and colored correlated noises can expedite the regime shift from the eutrophication to oligotrophication, thereby inhibiting the development of lake eutrophication and protecting the stability of lake ecosystem.