Open Access

On the system of rational difference equations xn+1 = f(x n ,yn-k), yn+1 = f(y n , xn-k)

Advances in Difference Equations20062006:016949

DOI: 10.1155/ADE/2006/16949

Received: 15 September 2005

Accepted: 13 November 2005

Published: 23 February 2006

Abstract

We study the global asymptotic behavior of the positive solutions of the system of rational difference equations xn+1 = f(x n ,yn-k), yn+1 = f(y n , xn-k), n = 0,1,2,..., under appropriate assumptions, where k {1,2,...} and the initial values x-k, x-k+1,...,x0, y-k, y-k+1, ..., y0 (0,+∞). We give sufficient conditions under which every positive solution of this equation converges to a positive equilibrium. The main theorem in [1] is included in our result.

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Authors’ Affiliations

(1)
Department of Mathematics, Guangxi University
(2)
Department of Mathematics, Guangxi College of Finance and Economics

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Copyright

© Taixiang Sun et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.