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

Year 2020, Volume: 8 Issue: 1, 79 - 90, 15.04.2020

İnci Okumuş , Yüksel Soykan

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.

Keywords

difference equations; equilibrium point; global asymptotic stability; solutions; tribonacci number

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