Abstract
In this thesis, we investigate a mathematical model of two species competing in a chemostat for one resource that is stored internally, where one of the species can act as an intraguild predator that also feeds on the other species. We utilize theory of uniform persistence to prove that coexistence is possible under some suitable conditions, and our numerical simulations also confirm theoretical results. It is worth noting that Smith and Waltman proved that competitive exclusion holds for the classical model without predation, that is, the species that can grow at the lowest nutrient concentration will win the competition. From our study, intraguild predation may promote the possibility of coexistence.