Dynamic Behavior and Bifurcation Analysis of a Modified Reduced Lorenz Model

Mohammed O. Al-Kaff (), Ghada AlNemer (), Hamdy A. El-Metwally, Abd-Elalim A. Elsadany and Elmetwally M. Elabbasy
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Mohammed O. Al-Kaff: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
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
Elmetwally M. Elabbasy: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2024, vol. 12, issue 9, 1-20

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.

Keywords: Lorenz model; pitchfork bifurcation; period-doubling; Neimark–Sacker bifurcation; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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