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Computational Ecology and Software, 2014, 4(2): 89-103
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Article

Stability analysis of a discrete ecological model

Q. Din1 , E. M. Elsayed2,3
1Department of Mathematics, Faculty of Basic and Applied Sciences, University of PoonchRawalakot, Pakistan
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received 14 January 2014;Accepted 20 February 2014;Published online 1 June 2014
IAEES

Abstract
In this paper, we study the qualitative behavior of following discrete-time population model: xn+1=a+bxn+rxn-1exp-y(n),yn-1=g+eyn+hyn-1exp-x(n), where parameters a, b, r, g, e, h and initial conditions x0, x-1, y0, y-1 are positive real numbers. More precisely, we investigate the existence and uniqueness of positive equilibrium point,boundedness character, persistence, local asymptotic stability, global behavior and rate of convergence of unique positive equilibrium point of this model. Some numerical examples are given to verify our theoretical results.

Keywords population models;difference equations;steady-states;boundedness;local and global character.


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