Advances in Difference Equations
Volume 2009 (2009), Article ID 132802, 30 pages
doi:10.1155/2009/132802
Research Article

Global Dynamics of a Competitive System of Rational Difference Equations in the Plane

S. Kalabušić,1 M. R. S. Kulenović,2 and E. Pilav1

1Department of Mathematics, University of Sarajevo, 71 000 Sarajevo, Bosnia and Herzegovina
2Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

Received 26 August 2009; Accepted 8 December 2009

Academic Editor: Panayiotis Siafarikas

Copyright © 2009 S. Kalabušić et al. 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.

Abstract

We investigate global dynamics of the following systems of difference equations xn+1=(α1+β1xn)/yn, yn+1=(α2+γ2yn)/(A2+xn), n=0,1,2,…, where the parameters α1, β1, α2, γ2, and A2 are positive numbers and initial conditions x0 and y0 are arbitrary nonnegative numbers such that y0>0. We show that this system has rich dynamics which depend on the part of parametric space. We show that the basins of attractions of different locally asymptotically stable equilibrium points are separated by the global stable manifolds of either saddle points or of nonhyperbolic equilibrium points.