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Dynamic Behavior and Bifurcation Analysis of a Modified Reduced Lorenz Model

Author

Listed:
  • Mohammed O. Al-Kaff

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, College of Education, Seiyun University, Seiyun, Yemen)

  • Ghada AlNemer

    (Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia)

  • Hamdy A. El-Metwally

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Abd-Elalim A. Elsadany

    (Mathematics Department, College of Science and Humanities Studies Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt)

  • Elmetwally M. Elabbasy

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

This study introduces a newly modified Lorenz model capable of demonstrating bifurcation within a specified range of parameters. The model demonstrates various bifurcation behaviors, which are depicted as distinct structures in the diagram. The study aims to discover and analyze the existence and stability of fixed points in the model. To achieve this, the center manifold theorem and bifurcation theory are employed to identify the requirements for pitchfork bifurcation, period-doubling bifurcation, and Neimark–Sacker bifurcation. In addition to theoretical findings, numerical simulations, including bifurcation diagrams, phase pictures, and maximum Lyapunov exponents, showcase the nuanced, complex, and diverse dynamics. Finally, the study applies the Ott–Grebogi–Yorke (OGY) method to control the chaos observed in the reduced modified Lorenz model.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1354-:d:1385770
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    References listed on IDEAS

    as
    1. Zhang, Limin & Zhang, Chaofeng & He, Zhirong, 2019. "Codimension-one and codimension-two bifurcations of a discrete predator–prey system with strong Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 155-178.
    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. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
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