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.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Articles |
Authors | |
Publication Date | December 26, 2019 |
Submission Date | September 29, 2019 |
Acceptance Date | November 5, 2019 |
Published in Issue | Year 2019 |
Universal Journal of Mathematics and Applications
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