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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

https://doi.org/10.1155/ADE/2006/16949

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

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.

Keywords

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

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Authors’ Affiliations

(1)
Department of Mathematics, Guangxi University, Nanning, Guangxi, 530004, China
(2)
Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi, 530004, China

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