IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3810-d1534877.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3810/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3810/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3810-:d:1534877. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.