On the Solutions of Systems of Rational Difference Equations

E. M. Elsayed; J. G. Al-Juaid; H. Malaikah

E. M. Elsayed Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, KSA https://orcid.org/0000-0003-0894-8472
J. G. Al-Juaid Department of Mathematics, Faculty of Sciences, Mansoura University, Mansoura 35516, Egypt https://orcid.org/0000-0001-6062-5916
H. Malaikah Department of Mathematics, Faculty of Sciences, Taif University, P. O. Box 11099, Taif 21944, KSA

Keywords: Solutions of difference equations, periodic solution, recursive sequences.

Abstract

In this paper we study the form of the solutions of the following systems of difference equations

w_{n+1}=\frac{s_{n}(w_{n-3}+s_{n-4})}{s_{n-4}+w_{n-3} -s_{n}} , s_{n+1}=\frac{w_{n-2}(w_{n-2}+s_{n-3})}{2*w_{n-2}+s_{n-3}}.

w_{n+1}=\frac{(s_{n-4} - w_{n-3})s_{n}}{s_{n-4} -w_{n-3} +s_{n}} , s_{n+1}=\frac{(s_{n-3} - w_{n-2})w_{n-2}}{s_{n-3}}.

With nonzero real numbers initial conditions.

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