Geodesic
On solutions of a system of rational difference equations
Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 1 
Yu Yang; Li Chen; Yong-Guo Shi. On solutions of a system of rational difference equations. Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2011_80_1_a4/
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     author = {Yu Yang and Li Chen and Yong-Guo Shi},
     title = {On solutions of a system of rational difference equations},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2011},
     volume = {80},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2011_80_1_a4/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper we investigate the system of rational difference equations where q is a positive integer with p < q , p \not | q , p is an odd number and p 3 3, both a and b are nonzero real constants and the initial values x -q+1 , x -q+2 , . . . x 0 , y -q+1 , y -q+2 , . . ., y 0 are nonzero real numbers. We show all real solutions of the system are eventually periodic with period 2 pq (resp. 4 pq ) when (a/b)q = 1 (resp. (a/b)q = -1), characterize the asymptotic behavior of the solutions when a 3 b , which generalizes Őzban's results of in [Appl. Math. Comput. 188 (2007), 833-837].