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  • Research Article
  • Open Access

Asymptotic behavior of a competitive system of linear fractional difference equations

Advances in Difference Equations20062006:019756

  • Received: 18 July 2005
  • Accepted: 5 April 2006
  • Published:


We investigate the global asymptotic behavior of solutions of the system of difference equations xn+1 = (a+x n )/(b+y n ), yn+1 = (d+y n )/(e+x n ), n = 0,1,..., where the parameters a, b, d, and e are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. In certain range of parameters, we prove the existence of the global stable manifold of the unique positive equilibrium of this system which is the graph of an increasing curve. We show that the stable manifold of this system separates the positive quadrant of initial conditions into basins of attraction of two types of asymptotic behavior. In the case where a = d and b = e, we find an explicit equation for the stable manifold to be y = x.


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


Authors’ Affiliations

Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA
Department of Mathematics, University of Tuzla, Tuzla, 75000, Bosnia and Herzegovina


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© M. R. S. Kulenović and Nurkanović 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.