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

Author

Listed:
  • 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
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

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.

Suggested Citation

  • Khalil S. Al-Basyouni & Elsayed M. Elsayed, 2023. "On Some Solvable Systems of Some Rational Difference Equations of Third Order," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1047-:d:1073324
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    References listed on IDEAS

    as
    1. H. El-Metwally, 2013. "Solutions Form for Some Rational Systems of Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-10, May.
    2. E. M. Elsayed, 2011. "Solution and Attractivity for a Rational Recursive Sequence," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-17, June.
    3. Abdulrahman Al-Khedhairi & Abdelalim A. Elsadany & Amr Elsonbaty & Ali Ahmadian, 2022. "On the Dynamics of a Discrete Fractional-Order Cournot–Bertrand Competition Duopoly Game," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-13, February.
    4. Banyat Sroysang, 2013. "Dynamics of a System of Rational Higher-Order Difference Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-5, May.
    5. M. Mansour & M. M. El-Dessoky & E. M. Elsayed, 2012. "The Form of the Solutions and Periodicity of Some Systems of Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-17, August.
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    Cited by:

    1. Hashem Althagafi & Ahmed Ghezal, 2024. "Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations," Mathematics, MDPI, vol. 12(8), pages 1-20, April.

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