Global behavior of a third-order rational difference equation

Volume 25, Issue 3, pp 296--302 http://dx.doi.org/10.22436/jmcs.025.03.08
Publication Date: July 03, 2021 Submission Date: April 01, 2021 Revision Date: May 23, 2021 Accteptance Date: June 16, 2021

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.


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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


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