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Computational Ecology and Software, 2014, 4(1): 35-46
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Article

Global behavior of an anti-competitive system of fourth-order rational difference equations

A. Q. Khan1, Q. Din1, M. N. Qureshi1, T. F. Ibrahim2,3
1Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, Pakistan
2Department of Mathematics, Faculty of Sciences and Arts King Khalid University, Abha, Saudi Arabia
3Permanent address: Department of Mathematics, Faculty of Sciences Mansoura University, Mansoura 35516, Egypt

Received 22 October 2013;Accepted 28 November 2013;Published online 1 March 2014
IAEES

Abstract
In the present work, we study the qualitative behavior of an anti-competitive system of fourth-order rational difference equations. More precisely, we study the local asymptotic stability, global character of the unique equilibrium point, and the rate of convergence of the positive solutions of the given system. Some numerical examples are given to verify our theoretical results.

Keywords system of rational difference equations;stability;global character;rate of convergence.



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