Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 153058, 34 pages
doi:10.1155/2009/153058
Global behavior of four competitive rational systems of difference equations in the plane
M. Garić-Demirović1
, M.R.S. Kulenović2
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
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).