具有分离扩散的两种群Lotka-Volterra模型的持久性

The Persistence of Two Species Lotka-Volterra Model with Diffusion

本文考虑具有分离扩散的捕食-被捕食系统的持续性。此模型由两种群组成，其中被捕食种群可在两个生态环境中生存，而捕食种群仅能在一个生态环境中生存，两种群的动态行为都用Lotka－Volterra模型来描述。得到了系统强持续的充分必要条件，并证明了无论无扩散时系统是共存的，还是主导的都可以适当选择分离扩散系数使整个系统强持续。

In this paper,the authors consider a model in which need to forage and the need to avoid predated ane in conflict. The medel is composed two Lotka-Volterra patches.The system has two species, one can diffuse betteen two patches,but the other is confined to one of the patches and can not diffuse. the authors obtain the necessary and sufficent condition of the strong persistence of the system,and prove that the system can be made strong persistence under appropriate diffusion conditions that ensure the in stability of boundary equilibria,even if the preypredator patch is not persist without diffusion.