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December 2020 Global behavior of two-dimensional difference equations system with two period coefficients
Merve Kara, Durhasan Turgut Tollu, Yasin Yazlik
Tbilisi Math. J. 13(4): 49-64 (December 2020). DOI: 10.32513/tbilisi/1608606049

Abstract

In this paper, we investigate the following system of difference equations \begin{equation*} x_{n+1}=\frac{\alpha _{n}}{1+y_{n}x_{n-1}},\ y_{n+1}=\frac{\beta _{n}} {1+x_{n}y_{n-1}}, n\in \mathbb{N}_{0}, \end{equation*} where the sequences $\left( \alpha _{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( \beta_{n}\right) _{n\in \mathbb{N}_{0}}$ are positive, real and periodic with period two and the initial values $x_{-1}$, $x_{0}$, $y_{-1}$, $y_{0}$ are non-negative real numbers. We show that every positive solution of the system is bounded and examine their global behaviors. In addition, we give closed forms of the general solutions of the system by using the change of variables. Finally, we present a numerical example to support our results.

Citation

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Merve Kara. Durhasan Turgut Tollu. Yasin Yazlik. "Global behavior of two-dimensional difference equations system with two period coefficients." Tbilisi Math. J. 13 (4) 49 - 64, December 2020. https://doi.org/10.32513/tbilisi/1608606049

Information

Received: 20 March 2020; Accepted: 18 September 2020; Published: December 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4194228
Digital Object Identifier: 10.32513/tbilisi/1608606049

Subjects:
Primary: 39A10
Secondary: 39A20, 39A23

Rights: Copyright © 2020 Tbilisi Centre for Mathematical Sciences

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Vol.13 • No. 4 • December 2020
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