Abstract
We study a chemostat model that describes competition between n microbial species for a single-limited resource based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the fluctuating method. It is shown that the competitive exclusion principle holds for the limiting system of the model. The species with the smallest ambient nutrient concentration wins the competition. We extend the result of competitive exclusion in the paper [H. L. Smith and P. Waltmam, SIAM J. Appl. Math., 54 (1994), pp. 1113-1131] from two species to n species. © 2008 Society for Industrial and Applied Mathematics.