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

Authors : İnci OKUMUŞ, Yüksel SOYKAN

Pages : 79-90

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Publication Date : 2020-04-15

Article Type : Research Paper

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}\leftinsert ignore into journalissuearticles values( x_{n-1}\pm 1\right); \pm 1}\text{,} \\ x_{n+1} &=&\frac{-1}{x_{n}\leftinsert ignore into journalissuearticles values( 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