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Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

Author

Listed:
  • Hashem Althagafi

    (Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia)

  • Ahmed Ghezal

    (Department of Mathematics, University Center of Mila, Mila 43000, Algeria)

Abstract

This paper aims to derive analytical expressions for solutions of fractional bidimensional systems of difference equations with higher-order terms under specific parametric conditions. Additionally, formulations of solutions for one-dimensional equations derived from these systems are explored. Furthermore, rigorous proof is provided for the local stability of the unique positive equilibrium point of the proposed systems. The theoretical findings are validated through numerical examples using MATLAB, facilitating graphical illustrations of the results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1159-:d:1374595
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    References listed on IDEAS

    as
    1. 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.
    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.
    Full references (including those not matched with items on IDEAS)

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