離散和非局部競爭型洛特卡－沃爾泰拉系統的行波解之物種數量估計

Abstract

這篇論文主要是探討離散以及非局部的洛特卡-沃泰爾拉競爭模型的物種質量估計。這篇文章中，我們使用N型屏障方法去證明離散以及非局部的洛特卡-沃泰爾拉模型的物種有一個有意思的下界。除此之外，我們利用這個下界，我們能夠證明某些條件下，三個物種的洛特卡-沃泰爾拉模型的解是不存在的。

In the present paper, we show that an analogous N-barrier maximum principle (see [3,5,7]) remains true for lattice systems. This extends the results in [3,5,7] from continuous equations to discrete and non-local equations. In order to overcome the difficulty induced by a discrete and non-local version of the classical diffusion in the lattice and non-local systems, we propose a more delicate construction of the N-barrier which is appropriate for the proof of the N-barrier maximum principle for lattice systems. As an application of the discrete N-barrier maximum principle, we study a coexistence problem of three species arising from biology, and show that the three species cannot coexist under certain conditions.