Abstract
We study a mathematical model of two species competing in a chemostat for two internally stored essential nutrients, where the nutrients are added to the culture vessel by way of periodic forcing functions. Persistence of a single species happens if the nutrient supply is sufficient to allow it to acquire a threshold of average stored nutrient quota required for growth to balance dilution. More precisely, the population is washed out if a sub-threshold criterion holds, while there is a globally stable positive periodic solution, if a super-threshold criterion holds. When there is mutual invasibility of both semitrivial periodic solutions of the two-species model, both uniform persistence and the existence of periodic coexistence state are established.