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Computational Ecology and Software, 2014, 4(2): 104-115
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Article

Qualitative behavior of an anti-competitive system of third-order rational difference equations

Q. Din1 , M. N. Qureshi2 , A. Q. Khan2
1Department of Mathematics, Faculty of Basic and Applied Sciences, University of PoonchRawalakot, Pakistan
2Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, Pakistan

Received 6 December 2013;Accepted 10 January 2014;Published online 1 June 2014
IAEES

Abstract
In this paper, our aim is to study the equilibrium points, local asymptotic stability, global behavior of an equilibrium points and rate of convergence of an anti-competitive system of third-order rational difference equations of the form: xn+1=ayn-2/[b+rxnxn-1xn-2], yn+1=cxn-2/[d+hynyn-1yn-2], n=0,1,2,..., where the parameters a, b, c, d, r, h and initial conditions x0, x-1, x-2, y0, y-1, y-2 are positive real numbers. Some numerical examples are given to verify our theoretical results.

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


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