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

Authors : Mohamed ABD ELMONEAM

Pages : 31-43

Doi:10.33434/cams.1230130

View : 15 | Download : 11

Publication Date : 2023-03-31

Article Type : Research Paper

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