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

  • Ahmed Buseri Ashine Department of Mathematics, MaddaWalabu University, Bale Robe

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 is presented. The boundedness of solutions, qualitative properties, including local and global asymptotic stability of equilibriums of the system is proved by defining appropriate Dulac function is discussed. The paper also offers mathematical analysis of the model and discusses some significant qualitative results that are expected to arise from the interplay of biological forces. Numerical simulations are also carried out to verify the analytical results.
Published
2017-05-09
How to Cite
ASHINE, Ahmed Buseri. Mathematical Modeling of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes. Universal Journal of Mathematics, [S.l.], v. 2, n. 1, p. 137-154, may 2017. ISSN 2456-1312. Available at: <http://uproonline.com/index.php/UJM/article/view/75>. Date accessed: 22 sep. 2018.
Section
Articles

Keywords

Prey; Predator; Refuge Stability; Holling type II functional response; modified Leslie-Gower dynamics.