Displaying the Structure of the Solutions for Some Fifth-Order Systems of Recursive Equations

Abstract

This paper presents the solutions to the following nonlinear systems of rational difference equations: $x_{n+1}=\left(\left(x_{n-3}{y}_{n-4}\right)/\left(y_n\left(1+x_{n-1}{y}_{n-2}{x}_{n-3}{y}_{n-4}\right)\right)\right),y_{n+1}=\left(\left(y_{n-3}{x}_{n-4}\right)/\left(x_n\left(\pm 1\pm y_{n-1}{x}_{n-2}{y}_{n-3}{x}_{n-4}\right)\right)\right)$ where initial conditions $x_{-\delta },y_{-\delta }\left(\delta =\mathrm{4,3},\dots ,0\right)$ are nonnegative real numbers. Finally some numerical simulations are presented to verify obtained theoretical results.