Open Access

Asymptotic behavior of a competitive system of linear fractional difference equations

Advances in Difference Equations20062006:019756

DOI: 10.1155/ADE/2006/19756

Received: 18 July 2005

Accepted: 5 April 2006

Published: 30 August 2006


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.


Authors’ Affiliations

Department of Mathematics, University of Rhode Island
Department of Mathematics, University of Tuzla


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© M. R. S. Kulenović and Nurkanović 2006

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