On some rational systems of difference equations

Volume 11, Issue 1, pp 49--72 Publication Date: December 24, 2017       Article History
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Authors

M. M. El-Dessoky - Mathematics Department, Faculty of Science, King AbdulAziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. - Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt. 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.

Keywords

• Form of solution
• stability
• rational difference equations
• rational systems

•  39A10

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