Global Asymptotic Behavior of the Chemostat: General Response Functions and Different Removal Rates

In this paper, we consider a competition model between n species in a chemostat that incorporates both monotone and nonmonotone general response functions and distinct removal rates. We show that only the species with the lowest break-even concentration survives, provided that the variation of distinct removal rates relative to the flow rate of the chemostat can be controlled by either the difference between the two lowest break-even concentrations or by a parameter based on the structure of response functions. LaSalle’s extension theorem of the Lyapunov stability theory and fluctuation lemma are the main tools.