Global behavior of the difference equation $x_{n+1}=rac{ax_{n-3} }{b+ cx_{n-1}x_{n-3}}$

摘要

In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation [ x_{n+1}=rac{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.