In this paper, we solve and study the global behavior of all admissible solutions of the two difference equations $$x_{n+1}=\frac{x_{n}x_{n-2}}{x_{n-1}-x_{n-2}}, \quad n=0,1,...,$$ and $$x_{n+1}=\frac{x_{n}x_{n-2}}{-x_{n-1}+x_{n-2}}, \quad n=0,1,...,$$ where the initial values $x_{-2}$, $x_{-1}$, $x_{0}$ are real numbers.\\ We show that every admissible solution for the first equation converges to zero. For the other equation, we show that every admissible solution is periodic with prime period six. Finally we give some illustrative examples.
difference equation forbidden set periodic solution convergence
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 26 Aralık 2019 |
Gönderilme Tarihi | 29 Eylül 2019 |
Kabul Tarihi | 5 Kasım 2019 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 4 |
Universal Journal of Mathematics and Applications
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