Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 153058, 34 pages
doi:10.1155/2009/153058
Research Article

Global Behavior of Four Competitive Rational Systems of Difference Equations in the Plane

M. Garić-Demirović,1 M. R. S. Kulenović,2 and M. Nurkanović1

1Department of Mathematics, University of Tuzla, 75000 Tuzla, Bosnia And Herzegovina
2Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

Received 29 August 2009; Accepted 27 October 2009

Academic Editor: Guang Zhang

Copyright © 2009 M. Garić-Demirović 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 the global dynamics of solutions of four distinct competitive rational systems of difference equations in the plane. 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 nonhyperbolic equilibrium points. Our results give complete answer to Open Problem 2 posed recently by Camouzis et al. (2009).