Global Behavior of a Rational Difference Equation with Quadratic Term
Mathematica Moravica, Tome 18 (2014) no. 1.

Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of all solutions of the difference equation $x_{n+1} = \frac{ax_{n}x_{n-1}}{bx_{n}-cx_{n-2}},\qquad n=0,1,\dots$ where $a,b,c$ are positive real numbers and the initial conditions $x_{-2},x_{-1},x_{0}$ are real numbers. 
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     author = {R. Abo-Zeid},
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R. Abo-Zeid. Global Behavior of a Rational Difference Equation with Quadratic Term. Mathematica Moravica, Tome 18 (2014) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2014_18_1_a8/