Department of Mathematics, University of Thessaly, Lamia, 35100 Fthiotis, Greece. Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA.
This paper delves into the analysis of two 3D dynamical systems of ordinary differential equations (ODEs), namely the Quasi-Geostrophic Omega Equation and the Lorenz-96 Model. The primary objective of this paper is to analyze the chaotic and non-chaotic behavior exhibited by the QG Omega Equation and the Lorenz-96 Model in three dimensions. Through numerical simulations and analytical techniques, the author aimed to characterize the existence and properties of attractors within these systems and explore their implications for atmospheric dynamics. Also, the author has investigated how changes in initial conditions and system parameters influence the behavior of the dynamical systems. Furthermore, we investigate how changes in initial conditions and system parameters influence the behavior of the dynamical systems. Employing a combination of numerical simulations and analytical methods, including stability analysis and Lyapunov function, we uncover patterns and correlations that shed light on the mechanisms driving atmospheric phenomena. This analysis contributes to the understanding of atmospheric dynamics and has implications for weather forecasting and climate modeling, offering insights into the predictability and stability of atmospheric systems. Finally, We draw the phase portrait of the chaotic system and visualizations of the attractors of both systems. Concluding how the rigorous proofs of attractor existence as long as the matrix transformation of the system with the numerical methods followed may pave the way for future research in understanding and analyzing the behavior of chaotic weather models.
Gkrekas, N. (2024). Analysis of a chaotic and a non-chaotic 3D dynamical system: The Quasi-Geostrophic Omega Equation and the Lorenz-96 model. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2024.61295.2634
MLA
Nikolaos Gkrekas. "Analysis of a chaotic and a non-chaotic 3D dynamical system: The Quasi-Geostrophic Omega Equation and the Lorenz-96 model". Computational Methods for Differential Equations, , , 2024, -. doi: 10.22034/cmde.2024.61295.2634
HARVARD
Gkrekas, N. (2024). 'Analysis of a chaotic and a non-chaotic 3D dynamical system: The Quasi-Geostrophic Omega Equation and the Lorenz-96 model', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2024.61295.2634
VANCOUVER
Gkrekas, N. Analysis of a chaotic and a non-chaotic 3D dynamical system: The Quasi-Geostrophic Omega Equation and the Lorenz-96 model. Computational Methods for Differential Equations, 2024; (): -. doi: 10.22034/cmde.2024.61295.2634
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