A chemostat model of n species of microorganisms competing for two perfectly complementary, growth-limiting nutrients is considered. Sufficient conditions are given for there to be a single winning species and for two species to coexist, driving the others to extinction. In the case when n=3, it is shown that every solution converges to one of the single-species or two-species steady states, and hence the dynamics of the model is completely determined. The results generalize those of Hsu, Cheng, and Hubbell [SIAM J. Appl. Math., 41 (1981), pp. 422--444] as well as Butler and Wolkowicz [ Math. Biosci., 83 (1987), pp. 1--48] who considered two species.
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Li et al. (2001) studied this question.
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