Global Dynamical Properties of a System of Quadratic-Rational Difference Equations With Arbitrary Delay

Abstract

In this paper, we investigate the global dynamics of the following system of quadratic-higher order difference equations:\begin{equation*}x_{n+1}=A+B\frac{y_{n}}{y_{n-m}^{2}},y_{n+1}=A+B\frac{x_{n}}{x_{n-m}^{2}}\end{equation*}where $A$ and $B$ are positive numbers and the initial values are positive numbers. We first examine the existence of bounded solutions of the system. Additionally, we study the stability analysis of the of solutions of the system. We also analyze the rate of convergence and oscillation behavior of the solutions of the system.