Determining the competition outcome in the chemostat: General response functions and delayed growth

Competitive exclusion has been proven to be true mainly for competition in the chemostat with monotone response functions. For the case with nonmonotone response functions, strong restrictions are imposed on the property of response functions in the literature to ensure the competitive exclusion. In this work, by constructing a novel Liapunov functional, we show that only one species can survive when n species are competing for a single essential resource in the chemostat. The conditions are quite generic and our result applies to chemostat competition models with differential removal rates, delayed growth, and a large class of general response functions including the simplified Holling type IV response functions.