Abstract:
Based on the practice of controlling water quality, a kind of nutrition-phytoplankton model with nutrient cycle and state feedback control was established on the basis of the chemostat model. Firstly, the qualitative and stability of the continuous model were studied, and the conditions for the existence and stability of equilibria were given.Then, by using the theory of semi-continuous dynamical system and the method of successor function, the conditions under which the model has an unique and asymptotically stable periodic solution were obtained. Numerical simulations verified the theoretical results. The results showed that the phytoplankton such as algae can be controlled below the given threshold under the state feedback control.