American Institute of Mathematical Sciences

Advanced
2006, 3(1): 111-123. doi: 10.3934/mbe.2006.3.111

A competition model of the chemostat with an external inhibitor

Jianquan Li 1, , Zuren Feng 2, , Juan Zhang 1, and  Jie Lou 1,

1. 

Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China, China, China
2. 

Systems Engineering Institute, Xi'an Jiaotong University, Xi'an 710049, China

Received  December 2004 Revised  April 2005 Published  November 2005

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.
Keywords: stability, limit cycle., competition, chemostat.
Mathematics Subject Classification: 92D3.
Citation: Jianquan Li, Zuren Feng, Juan Zhang, Jie Lou. A competition model of the chemostat with an external inhibitor. Mathematical Biosciences & Engineering, 2006, 3 (1) : 111-123. doi: 10.3934/mbe.2006.3.111
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