Periodic solution of a chemostat model with Monod growth rate and impulsive state feedback control

In this paper, we develop a mathematical model concerning a chemostat with impulsive state feedback control to investigate the periodicity of bioprocess. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions under which the model has a periodic solution of order one are obtained. Furthermore, we estimate the position of the periodic solution of order one and discuss the existence of periodic solution of order two. The theoretical results and numerical simulations indicate that the chemostat system with impulsive state feedback control either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentrations of microorganisms and substrate.