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Global Behavior of a Nonlinear System of Difference Equations

Year 2025, Volume: 8 Issue: 1, 43 - 54, 31.03.2025

Fatma Hilal Gümüş , Raafat Abo-zeid

Abstract

In this paper, we study the admissible solutions of the nonlinear system of difference equations $$x_{n+1}=\dfrac{y_{n}}{x_{n}},\quad y_{n+1}=\dfrac{y_{n} }{\check{a}x_{n}+\check{b}y_{n}},\quad n=0,1,\ldots,$$ where $\check{a}$, $\check{b}$ are real numbers and the initial values $x_{0},y_{0}$ are nonzero real numbers. In case $\check{b}<0$ and ${\check{a}}^2<-4\check{b}$, we show that there are eventually periodic solutions when either $tan^{-1}\frac{\sqrt{-4\check{b}-{\check{a}}^2}}{\check{a}} \in]\dfrac{\pi}{2},\pi[$ (with $\check{a}<0$) is a rational multiple of $\pi$ or $tan^{-1}\frac{\sqrt{-4\check{b}-{\check{a}}^2}}{\check{a}} \in]0,\dfrac{\pi}{2}[$ (with $\check{a}>0$) as well.

Keywords

System of difference equations Forbidden set Periodic solution Convergence

References

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Year 2025, Volume: 8 Issue: 1, 43 - 54, 31.03.2025

Fatma Hilal Gümüş , Raafat Abo-zeid

Abstract

References

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There are 33 citations in total.

Details

Primary Language English
Subjects Ordinary Differential Equations, Difference Equations and Dynamical Systems
Journal Section Articles
Authors

Fatma Hilal Gümüş 0000-0002-6329-7142

Raafat Abo-zeid 0000-0002-1858-5583

Early Pub Date March 29, 2025
Publication Date March 31, 2025
Submission Date July 22, 2024
Acceptance Date January 29, 2025
Published in Issue Year 2025 Volume: 8 Issue: 1

Cite

APA Gümüş, F. H., & Abo-zeid, R. (2025). Global Behavior of a Nonlinear System of Difference Equations. Fundamental Journal of Mathematics and Applications, 8(1), 43-54.
AMA Gümüş FH, Abo-zeid R. Global Behavior of a Nonlinear System of Difference Equations. Fundam. J. Math. Appl. March 2025;8(1):43-54.
Chicago Gümüş, Fatma Hilal, and Raafat Abo-zeid. “Global Behavior of a Nonlinear System of Difference Equations”. Fundamental Journal of Mathematics and Applications 8, no. 1 (March 2025): 43-54.
EndNote Gümüş FH, Abo-zeid R (March 1, 2025) Global Behavior of a Nonlinear System of Difference Equations. Fundamental Journal of Mathematics and Applications 8 1 43–54.
IEEE F. H. Gümüş and R. Abo-zeid, “Global Behavior of a Nonlinear System of Difference Equations”, Fundam. J. Math. Appl., vol. 8, no. 1, pp. 43–54, 2025.
ISNAD Gümüş, Fatma Hilal - Abo-zeid, Raafat. “Global Behavior of a Nonlinear System of Difference Equations”. Fundamental Journal of Mathematics and Applications 8/1 (March 2025), 43-54.
JAMA Gümüş FH, Abo-zeid R. Global Behavior of a Nonlinear System of Difference Equations. Fundam. J. Math. Appl. 2025;8:43–54.
MLA Gümüş, Fatma Hilal and Raafat Abo-zeid. “Global Behavior of a Nonlinear System of Difference Equations”. Fundamental Journal of Mathematics and Applications, vol. 8, no. 1, 2025, pp. 43-54.
Vancouver Gümüş FH, Abo-zeid R. Global Behavior of a Nonlinear System of Difference Equations. Fundam. J. Math. Appl. 2025;8(1):43-54.
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