A competition model of the chemostat with an external inhibitor

Jianquan Li; Zuren Feng; Juan Zhang; Jie Lou; Jianquan Li; Zuren Feng; Juan Zhang; Jie Lou

doi:10.3934/mbe.2006.3.111

Mathematical Biosciences and Engineering

2006, Volume 3, Issue 1: 111-123. doi: 10.3934/mbe.2006.3.111

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A competition model of the chemostat with an external inhibitor

1.
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049
2.
Systems Engineering Institute, Xi'an Jiaotong University, Xi'an 710049

Received: 01 December 2004 Accepted: 29 June 2018 Published: 01 November 2005
MSC : 92D30.

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.
- stability,
- limit cycle.,
- competition,
- chemostat
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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