Geodesic
Global behavior of the difference equation $x_{n+1}=\frac{ax_{n-3} }{b+ cx_{n-1}x_{n-3}}$
Archivum mathematicum, Tome 51 (2015) no. 2, pp. 77-85.

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In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation \[ x_{n+1}=\frac{ax_{n-3} }{b+ cx_{n-1}x_{n-3}}\,,\qquad n=0,1,\dots \] where $a,b,c$ are positive real numbers and the initial conditions $x_{-3}$, $x_{-2}$, $x_{-1}$, $x_0$ are real numbers.
DOI : 10.5817/AM2015-2-77
Classification : 39A20, 39A21, 39A23, 39A30
Keywords: difference equation; periodic solution; convergence 
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Abo-Zeid, Raafat. Global behavior of the difference equation $x_{n+1}=\frac{ax_{n-3} }{b+ cx_{n-1}x_{n-3}}$. Archivum mathematicum, Tome 51 (2015) no. 2, pp. 77-85. doi : 10.5817/AM2015-2-77. http://geodesic.mathdoc.fr/articles/10.5817/AM2015-2-77/

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