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

Wolkowicz, Gail S. K.; Zhao, Xiao-Qiang

Differ. Integral Equ. 11, No. 3, 465-491 (1998).

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.

Reviewer: Bohdan Maslowski (Praha)

MSC:

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