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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 1-20, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2423-:d:1449695
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    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.
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