Coexistence of a three species predator-prey model with diffusion and density dependent mortality

摘要

In this paper, we consider a two competitor-one prey model with diffusion in which both competitors exhibit general functional response and one of the competitors exhibits density dependent mortality rate. By using the linearization method and Laypunov functional method, we study the local and global stability of the constant equilibrium, respectively. It is shown that the two competitors can coexistence upon one single prey. As an example, we consider a two competitor-one prey model with diffusion and Holling II functional response. Our results demonstrate that density-dependent mortality in one of the competitors can prevent competitive exclusion.