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Keywords:
difference equation; periodic solution; convergence
difference equation; periodic solution; convergence
Summary:
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.
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