On some rational systems of difference equations


Authors

M. M. El-Dessoky - Mathematics Department, Faculty of Science, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
A. Khaliq - Department of Mathematics, Riphah International University, Lahore, Pakistan
A. Asiri - Mathematics Department, Faculty of Science, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia


Abstract

Our goal in this paper is to find the form of solutions for the following systems of rational difference equations: \[ x_{n+1}=\frac{x_{n-3}y_{n-4}}{y_{n}(\pm 1\pm x_{n-3}y_{n-4})},\quad y_{n+1}=\frac{y_{n-3}x_{n-4}}{x_{n}(\pm 1\pm y_{n-3}x_{n-4})},\quad n=0,1,\ldots, \] where the initial conditions have non-zero real numbers.


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