On the Solutions of Four Rational Difference Equations Associated to Tribonacci Numbers

Abstract

In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following four rational difference equations% \begin{eqnarray*} x_{n+1} &=&\frac{1}{x_{n}\left( x_{n-1}\pm 1\right) \pm 1}\text{,} \\ x_{n+1} &=&\frac{-1}{x_{n}\left( x_{n-1}\pm 1\right) \mp 1}\text{,} \end{eqnarray*}% such that their solutions are associated with Tribonacci numbers.