On Some Solvable Systems of Some Rational Difference Equations of Third Order

Khalil S. Al-Basyouni and Elsayed M. Elsayed ()
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Khalil S. Al-Basyouni: Faculty of Science, Mathematics Department, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Elsayed M. Elsayed: Faculty of Science, Mathematics Department, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2023, vol. 11, issue 4, 1-13

Abstract: Our aim in this paper is to obtain formulas for solutions of rational difference equations such as x n + 1 = 1 ± x n − 1 y n / 1 − y n , y n + 1 = 1 ± y n − 1 x n / 1 − x n , and x n + 1 = 1 ± x n − 1 y n − 2 / 1 − y n , y n + 1 = 1 ± y n − 1 x n − 2 / 1 − x n , where the initial conditions x − 2 , x − 1 , x 0 , y − 2 , y − 1 , y 0 are non-zero real numbers. In addition, we show that the some of these systems are periodic with different periods. We also verify our theoretical outcomes at the end with some numerical applications and draw it by using some mathematical programs to illustrate the results.

Keywords: difference equations; periodicity nature; system of difference equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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