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).


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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


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