A qualitative investigation of some rational difference equations
Volume 34, Issue 1, pp 1--10
https://dx.doi.org/10.22436/jmcs.034.01.01
Publication Date: February 12, 2024
Submission Date: December 08, 2023
Revision Date: December 22, 2023
Accteptance Date: January 03, 2024
Authors
H. El-Metwally
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt.
M. T. Alharthi
- Department of Mathematics, Faculty of Science, Jeddah University, Jeddah, Saudi Arabia.
Abstract
In this paper we study some qualitative properties of the solutions for the
following difference equation
\[
y_{n+1}=\frac{\alpha +\alpha _{0} y_{n}^{r}+\alpha
_{1} y_{n-1}^{r}+\cdots+\alpha _{k} y_{n-k}^{r}}{\beta +\beta
_{0} y_{n}^{r}+\beta _{1} y_{n-1}^{r}+\cdots+\beta _{k} y_{n-k}^{r}}%
,~~~~n\geq 0,\tag{I}
\]
where \(r, \alpha , \alpha _{0}, \alpha _{1},\ldots, \alpha _{k},
\beta , \beta _{0}, \beta _{1},\ldots, \beta _{k}\in (0,\infty )\) and \(k \) is a non-negative integer number. We find the equilibrium points for the
considered equation. Then classify these points in terms of local stability
or not. We investigate the boundedness and the global stability of the
solutions for the considered equation. Also we study the existence of
periodic solutions of Eq. (I).
Share and Cite
ISRP Style
H. El-Metwally, M. T. Alharthi, A qualitative investigation of some rational difference equations, Journal of Mathematics and Computer Science, 34 (2024), no. 1, 1--10
AMA Style
El-Metwally H., Alharthi M. T., A qualitative investigation of some rational difference equations. J Math Comput SCI-JM. (2024); 34(1):1--10
Chicago/Turabian Style
El-Metwally, H., Alharthi, M. T.. "A qualitative investigation of some rational difference equations." Journal of Mathematics and Computer Science, 34, no. 1 (2024): 1--10
Keywords
- Boundedness
- local stability
- periodicity
- global stability
MSC
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