A competition model of the chemostat with an external inhibitor

  • 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.

    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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  • 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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    © 2006 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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