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
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.