Global dynamics of a nutrient-plankton system in the water ecosystem

To quantitatively study the relationship between nutritional enrichment and the oscillation of water quality, a new nutrient-plankton dynamics model is proposed in the light of a water ecosystem, such as the Three Gorges Reservoir Area. The derived results show that the plankton-free equilibrium is globally asymptotically stable if the concentration of the input nutrient is sufficient small. When nutrient recycling is absent, the zooplankton-free equilibrium is globally asymptotically stable for the middle concentration of the input nutrient, whereas the coexistent equilibrium is globally asymptotically stable for sufficient large concentration of the input nutrient. Furthermore, numerical simulation results confirm that the comprehensive effect of eutrophication by environmental pollution, nutrient recycling and excessive fishing intensity can induce the oscillation of water quality and the collapse of the water ecosystem.