Qualitative Behavior and Solutions of Sixth Rational Difference Equations

Abstract

In this article, we introduced the solutions of the following difference equations

$$z_{n+1}=\frac{z_{n-4}z_{n-5}}{z_{n}(\pm 1\pm z_{n-4}z_{n-5})}, n=0,1,2,...,$$

where the initial conditions $z_{-5},\ z_{-4},\ z_{-3},\ z_{-2,}\ z_{-1}$ and $z_{0}$ are arbitrary non-zero real numbers. Moreover, we presented the solutions of some special cases of these equations and studied the dynamic behavior of the these equations. Finally, we obtained the estimation of the initial coefficients.