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

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

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....

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Main Authors: Raid Kamel Naji, Salam Jasim Majeed
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2016/2010464
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spelling doaj-022733d34e7943ef966c89507983fb6c2020-11-24T23:20:35ZengHindawi LimitedInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/20104642010464The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey PopulationRaid Kamel Naji0Salam Jasim Majeed1Department of Mathematics, College of Science, Baghdad University, Baghdad, IraqDepartment of Mathematics, College of Science, Baghdad University, Baghdad, IraqWe 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.http://dx.doi.org/10.1155/2016/2010464
collection DOAJ
language English
format Article
sources DOAJ
author Raid Kamel Naji
Salam Jasim Majeed
spellingShingle Raid Kamel Naji
Salam Jasim Majeed
The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population
International Journal of Differential Equations
author_facet Raid Kamel Naji
Salam Jasim Majeed
author_sort Raid Kamel Naji
title The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population
title_short The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population
title_full The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population
title_fullStr The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population
title_full_unstemmed The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population
title_sort dynamical analysis of a prey-predator model with a refuge-stage structure prey population
publisher Hindawi Limited
series International Journal of Differential Equations
issn 1687-9643
1687-9651
publishDate 2016-01-01
description 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.
url http://dx.doi.org/10.1155/2016/2010464
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