Advances in Difference Equations
Volume 2011 (2011), Article ID 958602, 17 pages
doi:10.1155/2011/958602
Research Article

Dynamics of a Rational System of Difference Equations in the Plane

Ignacio Bajo,1 Daniel Franco,2 and Juan Perán2

1Departamento de Matemática Aplicada II, E.T.S.E. Telecomunicación, Universidade de Vigo, Campus Marcosende, 36310 Vigo, Spain
2Departamento de Matemática Aplicada, E.T.S.I. Industriales, UNED, C/ Juan del Rosal 12, 28040 Madrid, Spain

Received 10 December 2010; Accepted 21 February 2011

Academic Editor: Istvan Gyori

Copyright © 2011 Ignacio Bajo 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 consider a rational system of first-order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of the system. In particular, we discuss the boundedness and the asymptotic behavior of the solutions, the existence of periodic solutions, and the stability of equilibria.