\(N\)-species competition in a periodic chemostat. (English) Zbl 1005.92027

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.


92D25 Population dynamics (general)
37N25 Dynamical systems in biology
34C60 Qualitative investigation and simulation of ordinary differential equation models
34D99 Stability theory for ordinary differential equations