Nonlinear modelling of the interaction between phytoplankton and zooplankton with the impulsive feedback control

In this paper, a mathematical model including the phytoplankton and zooplankton with the impulsive feedback control is presented. The sufficient conditions for the existence of the order-1 and order-2 periodic solutions are obtained by using the geometrical theory of semi-continuous dynamic system. The stability of the order-1 periodic solution is discussed by the analogue of the Poincaré criterion. Finally, our results are justified by the numerical simulations.