A competition model of the chemostat with an external inhibitor
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Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049
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Systems Engineering Institute, Xi'an Jiaotong University, Xi'an 710049
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Received:
01 December 2004
Accepted:
29 June 2018
Published:
01 November 2005
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MSC :
92D30.
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A competition model of the chemostat with an external inhibitor
is considered. This inhibitor is lethal to one competitor and results in the
decrease of growth rate of this competitor. The existence and stability of the
extinction equilibria are discussed by using Liapunov function. The necessary
and sufficient condition guaranteeing the existence of the interior equilibrium
is given. It is found by numerical simulation that the system may be globally
stable or have a stable limit cycle if the interior equilibrium exists.
Citation: Jianquan Li, Zuren Feng, Juan Zhang, Jie Lou. A competition model of the chemostat with an external inhibitor[J]. Mathematical Biosciences and Engineering, 2006, 3(1): 111-123. doi: 10.3934/mbe.2006.3.111
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Abstract
A competition model of the chemostat with an external inhibitor
is considered. This inhibitor is lethal to one competitor and results in the
decrease of growth rate of this competitor. The existence and stability of the
extinction equilibria are discussed by using Liapunov function. The necessary
and sufficient condition guaranteeing the existence of the interior equilibrium
is given. It is found by numerical simulation that the system may be globally
stable or have a stable limit cycle if the interior equilibrium exists.
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