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International Journal of Differential Equations
Volume 2016 (2016), Article ID 2010464, 10 pages
http://dx.doi.org/10.1155/2016/2010464
Research Article

The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

1Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq
2Department of Physics, College of Science, Thi-Qar University, Nasiriyah, Iraq

Received 20 July 2016; Accepted 1 November 2016

Academic Editor: Jaume Giné

Copyright © 2016 Raid Kamel Naji and Salam Jasim Majeed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.