Asymptotic behavior and periodic nature of two difference equations

• Date: 2009
• Main Authors: Khalaf-Allah, R., Халаф-Аллах, Р.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3061
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We discuss the global asymptotic stability of the solutions of the difference equations $$x_{n+1} = \frac{x_{n−2}}{±1 + x_nx_{n−1}x_{n−2}}, \quad n = 0,1,…,$$ where the initial conditions $x_{−2}, x_{−1}, x_0$ are real numbers.