Behavior and Solution Representations of Fourth-Order Rational Systems of Difference Equations (European Journal of Pure and Applied Mathematics, 2025)
Our aim in this paper is to obtain formulas expressions for solutions of the difference equations. The purpose of this article is to determine the expressions of solutions for the following rational difference systems\[\Theta_{n+1} = \frac{\Theta_{n-2} \Omega_n}{\alpha \pm \Theta_{n-2} \pm \Omega_{n-3}}, \quad \Omega_{n+1} = \frac{\Theta_n \Omega_{n-2}}{\beta + \Theta_{n-3} + \Omega_{n-2}}, \quad n = 0, 1, 2, \ldots\]where the real numbers $\alpha$ and $\beta$ are arbitrary. Additionally, the qualitative behavior of the solutions is analyzed, including their boundedness as well as their local and global stability. We will illustrate our findings with numerical examples.