International Journal of Differential Equations

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

Raid Kamel Naji and Salam Jasim Majeed

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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.

Article information

Source
Int. J. Differ. Equ., Volume 2016 (2016), Article ID 2010464, 10 pages.

Dates
Received: 20 July 2016
Accepted: 1 November 2016
First available in Project Euclid: 21 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1482352604

Digital Object Identifier
doi:10.1155/2016/2010464

Mathematical Reviews number (MathSciNet)
MR3579220

Zentralblatt MATH identifier
06915916

Citation

Naji, Raid Kamel; Majeed, Salam Jasim. The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population. Int. J. Differ. Equ. 2016 (2016), Article ID 2010464, 10 pages. doi:10.1155/2016/2010464. https://projecteuclid.org/euclid.ijde/1482352604


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