## E. M. Elsayed and A. Alshareef, Qualitative behavior of a system of second order difference equations, Eur. J. Math. Appl. 1 (2021), Article ID 15.

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Volume 1 (2021), Article ID 15

https://doi.org/10.28919/ejma.2021.1.15

Published: 16/11/2021

Abstract:

In this paper, we deal with the following system of rational difference equations

$$\chi_{n+1}\,=\,{\alpha_1\,\chi_{n-1}\,\tau_{n-1}\over{\beta+\tau_{n-1}}}\,\,\,\,\,\,\text{and}\,\,\,\,\,\,\tau_{n+1}\,=\,{\alpha_{2}\,\chi_{n}\,\tau_{n}\over{\beta+\chi_{n}}},$$

where $\alpha_{1},\,\alpha_{2}$ and $\beta$ are real positive numbers and the initial conditions are $\chi_{0},\,\chi_{-1},\,\tau_{0}$ and $\tau_{-1}$. We show that the solutions of this system are bounded. Also, we prove that there is no periodic solutions of period two. Moreover, we investigate the local and global stability of the equilibrium point. Some numerical examples are given.

How to Cite:

E. M. Elsayed and A. Alshareef, Qualitative behavior of a system of second order difference equations, Eur. J. Math. Appl. 1 (2021), Article ID 15. https://doi.org/10.28919/ejma.2021.1.15