Global Asymptotic Stability of a System of Difference Equations with Quadratic Terms

Year 2023, Volume: 6 Issue: 1, 31 - 43, 31.03.2023

Mohamed Abd El-moneam

https://doi.org/10.33434/cams.1230130

Cited By: 1

Abstract

In this article, we discuss the global asymptotic stability of following system of difference equations with quadratic terms: $x_{i+1}=\alpha+\beta \frac{y_{i-1}}{y_{i}^{2}},\quad y_{i+1}=\alpha+\beta \frac{x_{i-1}}{x_{i}^{2} }$ where $\alpha$, $\beta$ are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system. We will give also, some numerical examples to illustrate our results.

Keywords

difference equations, Global asymptotic stability, system

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