Global stability of Leslie-Gower Predator-prey Model with Density Dependent Birth Rate on Prey Species and Prey Refuge

A Leslie-Gower predator prey model with density dependent birth rate on prey species and prey refuge is proposed and studied in this paper. Sufficient condition which ensure the global stable of the positive equilibrium is obtained. Our study indicates density dependent birth rate of prey species has negative effect on the final density of both prey and predator species. Density dependent birth rate may lead to the Allee effect of prey species and enhance the extinction chance of the species. Numeric simulations are carried out to show the feasibility of the main results.