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  • Research Article
  • 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

  • Received: 15 September 2005
  • Accepted: 13 November 2005
  • Published:


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.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Asymptotic Behavior


Authors’ Affiliations

Department of Mathematics, Guangxi University, Nanning, Guangxi, 530004, China
Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi, 530004, China


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© 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.