Geodesic
On the recursive system xn+1 = A + xn-m / yn, yn+1 = B + yn-m / xn
Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 2, pp. 201-208 
Qianhong Zhang; Lihui Yang; Jingzhong Liu; Qianhong Zhang; Lihui Yang; Jingzhong Liu. On the recursive system   xn+1 = A + xn-m / yn,   yn+1 = B + yn-m / xn. Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 2, pp. 201-208. http://geodesic.mathdoc.fr/item/AMUC_2013_82_2_a4/
@article{AMUC_2013_82_2_a4,
     author = {Qianhong Zhang and Lihui Yang and Jingzhong Liu and Qianhong Zhang and Lihui Yang and Jingzhong Liu},
     title = { On the recursive system   xn+1 = {A} + xn-m / yn,   yn+1 = {B} + yn-m / xn},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {201--208},
     year = {2013},
     volume = {82},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2013_82_2_a4/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper, we investigate the boundedness, persistence and global asymptotic stability of positive solutions of the system of two nonlinear difference equations xn+1 = A + xn-m / yn, yn+1 = B + yn-m / xn n = 0, 1, . . . where A, B Î (0,¥), xi Î (0,¥), yi Î (0,¥), i = -m, -m+1, . . ., 0.