Global behavior of a third-order rational difference equation
Authors
L. Sh. Aljoufi
- Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia.
A. M. Ahmed
- Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia.
- Department of Mathematics, Faculty of Science, Al Azhar University, Nasr City 11884, Cairo, Egypt.
S. Al Mohammady
- Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Jouf, Saudi Arabia.
- Department of Mathematics, Faculty of Science, Helwan University, Helwan 11795, Egypt.
Abstract
In this paper, we investigate the behavior of solutions of the difference equation
\[
x_{n+1}=\frac{\alpha \left( x_{n-1}+x_{n-2}\right) +\left( \alpha -1\right)
x_{n-1}x_{n-2}}{x_{n-1}x_{n-2}+\alpha },\;\ \ \ n=0,1,2,\ldots,
\]
where the initial conditions \(x_{-2},x_{-1},x_{0}\) are
arbitrary non-negative real numbers and the parameter \(\alpha \in \lbrack
1,\infty ).\) More precisely, we study the boundedness, stability, and
oscillation of the solutions of this equation.
Share and Cite
ISRP Style
L. Sh. Aljoufi, A. M. Ahmed, S. Al Mohammady, Global behavior of a third-order rational difference equation, Journal of Mathematics and Computer Science, 25 (2022), no. 3, 296--302
AMA Style
Aljoufi L. Sh., Ahmed A. M., Mohammady S. Al, Global behavior of a third-order rational difference equation. J Math Comput SCI-JM. (2022); 25(3):296--302
Chicago/Turabian Style
Aljoufi, L. Sh., Ahmed, A. M., Mohammady, S. Al. "Global behavior of a third-order rational difference equation." Journal of Mathematics and Computer Science, 25, no. 3 (2022): 296--302
Keywords
- Difference equations
- stability
- oscillation
MSC
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