Analysis of a chaotic and a non-chaotic 3D dynamical system: the Quasi-Geostrophic omega equation and the Lorenz-96 model

Document Type : Research Paper

Author

Department of Mathematics, University of Thessaly, Lamia, 35100 Fthiotis, Greece.

Abstract

This paper delves into analyzing 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 aims to characterize the existence and properties of attractors within these systems and explore their implications for atmospheric dynamics. 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 functions,the author uncovers 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, the author presents the phase portrait of the chaotic system and visualizations of the attractors of both systems.

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Main Subjects

Computational Methods for Differential Equations
Volume 13, Issue 3
July 2025
Pages 721-741

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History

  • Receive Date: 20 April 2024
  • Revise Date: 05 June 2024
  • Accept Date: 20 July 2024

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