在弱捕食下兩競爭物種的慢移動者存活現象

Abstract

慢移動者存活現象自從 [1]Dockery 等人在 1988 年的文章開啟先鋒後已被廣泛研究，但當物種數目大於 2 時，問題至今仍未解。在這篇論文我們呈現兩個主題，第一部份我們研討著名的慢移動者存活現象，但不同以往的純粹競爭，我們考慮的模型加入獵食-捕食的元素，假定一種獵食者弱捕食兩相互競爭資源的物種，這兩競爭物種有不同的擴散速率，我們成功證明移動較慢的物種最後會存活而較快的物種會滅絕；第二部分我們拓展了 [2]Lam 和 Lou 的變異選擇模型，將擴散係數推廣為平滑的凸函數，在這樣的一般化下，我們仍可得到物種密度會隨著變異縮小而收斂，且這收斂速度不同於 [2] 的結果。

The slower diffuser phenomenon has been widely investigated since the pioneering work [1] by Dockery et al. which was published in 1998. However, when the number of species is larger than or equal to three, the problem is still unsolved. In this dissertation, we present two different topics. In part one, we study the famous slower diffuser phenomenon of 2 competing species under weak predation. We consider a predator-prey system of one predator and two preys with different diffusion rates. For this problem we successfully prove that the slower prey still prevails and wipes out the fast one as time goes to infinity. Part two deals with the mutation selection model described by Lam and Lou in [2] ,where the diffusion rate is generalized to a convex function of the mutation parameter. For this case, we are still able to establish the convergence of population density as the mutation gradually vanishes and find the new convergence rate is different from the one obtained by Lam and Lou.