论文标题
Lotka-Volterra竞争模型有限图
Lotka-Volterra competition models on finite graphs
论文作者
论文摘要
在本文中，我们研究了有限连接的图形，具有Dirichlet，Neumann或无边界条件的两个竞争物种Lotka-Volterra竞争模型。我们得到的是，当时间到达无穷大时，一个人会灭绝，而另一个则可以生存，或者两个竞争的物种共存，这至关重要的是物种的竞争力和在诺伊曼边界条件下的初始种群的大小以及没有边界条件的条件。我们的结果之一部分回答了[Siam J. Appl。 dyn。 Syst。，19（2020）]。我们主要结果证明的关键技术是上层和下溶液方法，这些方法是为有限图上的弱耦合抛物线系统开发的。
In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that when time goes to infinity, either one specie extincts while the other becomes surviving or both competing species coexist, which depend crucially on the strengh of species' competitiveness and the size of the initial population under the Neumann boundary condition and the condition that there is no boundary condition. One of our results partially answer a question posed by Slav\'ık in [SIAM J. Appl. Dyn. Syst., 19 (2020)]. The critical techiniques in the proof of our main results are upper and lower solutions method, which are developed for weakly coupled parabolic systems on finite graphs in this article.
