本篇論文主要是在探討，Michaelis-Menten形式的捕食者與被捕食者有著比例相關的生態模型的進行波解。我們討論在何種情況下，其進行波解會存在。另外也說明在某種情況下，並不存在某些特定的進行波解。
本論文的方向與結果，主要是來自於許世壁教授於2002年發表的論文【7】中的啟示，我們去猜想若在原來的反應方程組中加上擴散項的變數，是否會有進行波解的產生。我們發現在一些係數之間的確會有進行波產生，另外也證明了在一些充分條件下，有幾種進行波並不會發生。

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