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

Ahmed Buseri Ashine

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.


Keywords


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

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Copyright (c) 2017 Ahmed Buseri Ashine