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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/640594 |
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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |