Periodic solutions for a delayed competitive chemostat model with periodic nutrient input and rate

A nonautonomous periodic chemostat model with delays modelling $n$ species in competition is considered. Sufficient conditions on the coefficients and consumption functions for the species are given, for both the extinction of the species and for the existence of $n$ nontrivial and nonnegative periodic solutions. Further criteria guarantee that the system admits at least one strictly positive periodic solution.