IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i15p2423-d1449695.html
   My bibliography  Save this article

Research on Stability and Bifurcation for Two-Dimensional Two-Parameter Squared Discrete Dynamical Systems

Author

Listed:
  • Limei Liu

    (College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China)

  • Xitong Zhong

    (College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China)

Abstract

This study investigates a class of two-dimensional, two-parameter squared discrete dynamical systems. It determines the conditions for local stability at the fixed points for these proposed systems. Theoretical and numerical analyses are conducted to examine the bifurcation behavior of the proposed systems. Conditions for the existence of Naimark–Sacker bifurcation, transcritical bifurcation, and flip bifurcation are derived using center manifold theorem and bifurcation theory. Results of the theoretical analyses are validated by numerical simulation studies. Numerical simulations also reveal the complex bifurcation behaviors exhibited by the proposed systems and their advantage in image encryption.

Suggested Citation

  • Limei Liu & Xitong Zhong, 2024. "Research on Stability and Bifurcation for Two-Dimensional Two-Parameter Squared Discrete Dynamical Systems," Mathematics, MDPI, vol. 12(15), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2423-:d:1449695
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/15/2423/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/15/2423/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Ying-Qian & He, Yi & Wang, Xing-Yuan, 2018. "Spatiotemporal chaos in mixed linear–nonlinear two-dimensional coupled logistic map lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 148-160.
    2. Elsadany, A.A. & Yousef, A.M. & Elsonbaty, Amr, 2018. "Further analytical bifurcation analysis and applications of coupled logistic maps," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 314-336.
    3. Yamina Soula & Hadi Jahanshahi & Abdullah A. Al-Barakati & Irene Moroz, 2023. "Dynamics and Global Bifurcations in Two Symmetrically Coupled Non-Invertible Maps," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    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.
    1. Yao, Xiao-Yue & Li, Xian-Feng & Jiang, Jun & Leung, Andrew Y.T., 2022. "Codimension-one and -two bifurcation analysis of a two-dimensional coupled logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Mohammed O. Al-Kaff & Ghada AlNemer & Hamdy A. El-Metwally & Abd-Elalim A. Elsadany & Elmetwally M. Elabbasy, 2024. "Dynamic Behavior and Bifurcation Analysis of a Modified Reduced Lorenz Model," Mathematics, MDPI, vol. 12(9), pages 1-20, April.
    3. Dong, Youheng & Zhao, Geng, 2021. "A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Hongyan Zang & Jianying Liu & Jiu Li, 2021. "Construction of a Class of High-Dimensional Discrete Chaotic Systems," Mathematics, MDPI, vol. 9(4), pages 1-20, February.

    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:15:p:2423-:d:1449695. 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.