\(N\)-species competition in a periodic chemostat (Q1978212)

Global dynamics of the scalar, asymptotically periodic Kolmogorov equation is investigated and applications to models of single-species growth and \(n\)-species competition in a periodically operated chemostat are given. The theory of of asymptotically periodic semiflows and comparison methods are applied to obtain criteria that guarantee the existence of at least one positive periodic solution for the full system and uniform persistence of all the interacting species. In a special case, the single-species growth model has a threshold between global extinction and uniform persistence, in the form of a positive, periodic coexistence state.