Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 640594, 18 pages
doi:10.1155/2010/640594
Research Article

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

Yuan Tian,1,2 Kaibiao Sun,3 Andrzej Kasperski,4 and Lansun Chen2

1School of Information Engineering, Dalian University, Dalian 116622, China
2School of Mathematical Science, Dalian University of Technology, Dalian 116024, China
3School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China
4Faculty of Mathematics, Computer Science, and Econometrics, Bioinformatics Factory, University of Zielona Gora, Szafrana 4a, 65-516 Zielona Gora, Poland

Received 2 May 2010; Accepted 19 August 2010

Academic Editor: Francisco Solis

Copyright © 2010 Yuan Tian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.