Mathematical Modeling of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes

Abstract

In this paper, a two-dimensional continuous predator-prey system with Holling type II functional response and modified of Leslie –Gower type dynamics incorporating constant proportion of prey refuge compared by the model without refuge is proposed and analyzed. In both cases, by non-dimensionalize the system, the fixed points are computed and condition for local and global asymptotic stability of the system are obtained. Moreover, the global asymptotic stability of the system is proved by defining appropriate Dulac function. Numerical simulations are also carried out to verify the analytical results.