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Mathematical Biosciences and Engineering (MBE)
 

A competition model of the chemostat with an external inhibitor

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

 
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Jianquan Li - Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China (email)
Zuren Feng - Systems Engineering Institute, Xi'an Jiaotong University, Xi'an 710049, China (email)
Juan Zhang - Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China (email)
Jie Lou - Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China (email)

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.

Keywords:  competition, chemostat, stability, limit cycle.
Mathematics Subject Classification:  92D30.

Received: December 2004;      Accepted: April 2005;      Available Online: November 2005.