Open AccessA competition model of the chemostat with an external inhibitor
Author(s) -
Jianquan Li,
Zuren Feng,
Juan Zhang,
Jie Lou
Publication year - 2006
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2006.3.111
Subject(s) - chemostat , extinction (optical mineralogy) , competition (biology) , limit cycle , liapunov function , stability (learning theory) , limit (mathematics) , competition model , stability theory , mathematics , control theory (sociology) , mathematical economics , economics , ecology , physics , mathematical analysis , biology , computer science , microeconomics , nonlinear system , profit (economics) , genetics , control (management) , management , quantum mechanics , machine learning , bacteria , optics
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.