Analytical and Solutions of Fourth Order Difference Equations

Abstract

In this article, we presented the solutions of the following recursive sequences\[ x_{n+1}=\frac{x_{n-2}x_{n-3}}{x_{n}(\pm1\pm x_{n-2}x_{n-3})}, \] where the initial conditions $x_{-3}\ ,x_{-2}\ ,x_{-1}$\ and $x_{0}\ $are arbitrary real numbers. Also, we studied some dynamic behavior of these equations.