The Effect of Continuous and Pulse Input Nutrient on a Lake Model

In an aquatic environment, a mathematical model consisting of nutrient, phytoplankton, and zooplankton has been considered, where excretion of zooplankton is considered as one of the sources of nutrient. We investigate the effect of the input rate of the limiting nutrient from outside on controlling algal bloom. First, we consider input limiting nutrient continuously, obtain the system has two boundary equilibria, and analyze the existence of the positive equilibrium by means of stability analysis, we get conditions for the stability of the equilibria. Then, we consider input limiting nutrient impulsively. We get the exact expression of the boundary periodic solution and obtain the condition for the stability of the periodic boundary solution. We also consider the effect of temperature on the system and give a model of Taihu Lake as an example. Finally, we give numerical simulation of our results and explain the effect of input limiting nutrient on controlling bloom of the lake system