Analysis of a not so well-known chaotic dynamical system

Abstract

This thesis investigates a three-dimensional quadratic autonomous system proposed by Lü (2004), which exhibits Lorenz-like dynamics with unique structural features. Despite its initial introduction, critical aspects such as stability, bifurcation mechanisms, and transient chaos remain underexplored. Combining analytical and numerical methods, we derive equilibrium points, analyze their stability via the Routh-Hurwitz criterion, and identify supercritical Hopf bifurcations. Numerical validations, including Maximum Lyapunov exponent spectra and phase portraits, confirm chaotic regimes and multistability—coexistence of distinct attractors under fixed parameters. The results highlight the system’s dynamical richness, bridging periodic and chaotic states through parametric variations.This thesis investigates a three-dimensional quadratic autonomous system proposed by Lü (2004), which exhibits Lorenz-like dynamics with unique structural features. Despite its initial introduction, critical aspects such as stability, bifurcation mechanisms, and transient chaos remain underexplored. Combining analytical and numerical methods, we derive equilibrium points, analyze their stability via the Routh-Hurwitz criterion, and identify supercritical Hopf bifurcations. Numerical validations, including Maximum Lyapunov exponent spectra and phase portraits, confirm chaotic regimes and multistability—coexistence of distinct attractors under fixed parameters. The results highlight the system’s dynamical richness, bridging periodic and chaotic states through parametric variations.