Nonlinear Modelling and Qualitative Analysis of a Real Chemostat with Pulse Feeding

The control of substrate concentration in the bioreactor medium should be due to the substrate inhibition phenomenon. Moreover, the oxygen demand in a bioreactor should be lower than the dissolved oxygen content. The biomass concentration is one of the most important factors which affect the oxygen demand. In order to maintain the dissolved oxygen content in an appropriate range, the biomass concentration should not exceed a critical level. Based on the design ideas, a mathematical model of a chemostat with Monod-type kinetics and impulsive state feedback control for microorganisms of any biomass yield is proposed in this paper. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions for the existence of period-1 solution of the system are obtained. The results simplify the choice of suitable operating conditions for continuous culture systems. It also points out that the system is not chaotic according to the analysis on the existence of period-2 solution. The results and numerical simulations show that the chemostat system with state impulsive control tends to a stable state or a period solution.