Abstract
A competition model between two species with a lethal inhibitor in a chemostat is analyzed. Discrete delays are used to describe the nutrient conversion process. The proved qualitative properties of the solution are positivity, boundedness. By analyzing the local stability of equilibria, it is found that the conditions for stability and instability of the boundary equilibria are similar to those in [9]. In addition, the global asymptotic behavior of the system is discussed and the sufficient conditions for the global stability of the boundary equilibria are obtained. Moreover, by numerical simulation, it is interesting to find that the positive equilibrium may be globally stable.
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