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On the Dynamics of Some Higher-Order Nonlinear Difference Equations

Author

Listed:
  • Turki D. Alharbi

    (Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 24382, Saudi Arabia)

  • Md Rifat Hasan

    (Department of Applied Mathematics, Faculty of Science, Noakhali Science and Technology University, Noakhali 3814, Bangladesh)

Abstract

This research investigates the dynamics of higher-order nonlinear difference equations, specifically concentrating on seventh-order instances. Analytical solutions are obtained for particular equations, a formidable task owing to the absence of explicit mathematical techniques for their resolution. The qualitative characteristics of solutions, such as their stability, boundedness, and periodicity, are analysed by theoretical methods and numerical simulations. The results indicate that equilibrium points frequently lack local asymptotic stability, leading to intricate phenomena such as unbounded solutions and periodic attractors. These findings augment our understanding of nonlinear difference equations, offering significant implications for their use across various scientific fields.

Suggested Citation

  • Turki D. Alharbi & Md Rifat Hasan, 2024. "On the Dynamics of Some Higher-Order Nonlinear Difference Equations," Mathematics, MDPI, vol. 12(23), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3810-:d:1534877
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    References listed on IDEAS

    as
    1. H. S. Alayachi & M. S. M. Noorani & A. Q. Khan & M. B. Almatrafi, 2020. "Analytic Solutions and Stability of Sixth Order Difference Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, September.
    2. Lili Jia & Basil K. Papadopoulos, 2020. "Dynamic Behaviors of a Class of High-Order Fuzzy Difference Equations," Journal of Mathematics, Hindawi, vol. 2020, pages 1-13, April.
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