本論文主要探討兩個物種儲存內能競爭單一資源的數學模型，其中一個物種可以作為一個同功群間捕食者(intraguild predator)，它也吃其他的物種。我們利用 uniform persistence 的定理去證明在一些合適的條件下，這兩個物種共存是可能的，我們的數值模擬也證實了理論結果。值得注意的是，在參考文獻[18]或[19]中，已經證明在典型沒有捕食功能的模型中，物種會競爭排斥，也就是說，對資源濃度需求量最低的物種會單獨存活，而其他物種終將滅絕。從我們的研究中，同功群間捕食(intraguild predation)可促進物種共存的可能性。

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.

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