global-journal-of-science-frontier-research-f-mathematics-decision Global Journal of Science Frontier Research - F: Mathematics & Decision 0975-5896 2249-4626 Global Journals Publishing Group Incorporated 115595 Mathematical Modeling of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes AshineAhmed Buseri ETHIOPIA, Madda Walabu University 25 03 2017 17 F3

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.

 prey predator refuge stability holling type II functional response modified leslie-gower dynamics. Full Text

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.