| Titre : | Hidden Attractors and Hidden Bifurcation in Continuous Chaotic Systems |
| Auteurs : | Imene Saadi, Directeur de thèse ; ZAAMOUNE Faiza, Directeur de thèse |
| Type de document : | Mémoire magistere |
| Année de publication : | 2025 |
| Format : | 1 vol. (35 p.) |
| Langues: | Anglais |
| Mots-clés: | Nonlinear dynamics, chaos, hidden attractors, hidden bifurcation, strange attractor. |
| Résumé : |
This thesis provides a comprehensive examination of continuous dynamical systems, focusing on hidden attractors and hidden bifurcations, organized into three interconnected chapters. The initial chapter presents the essential concepts and characteristics of dynamical systems, subsequently categorizing equilibrium points and examining their stability. The notion of limit cycles is addressed as a fundamental aspect of dynamic behavior. The second chapter explores the concept of hidden attractors, beginning with self-excited attractors linked to unstable equilibrium points. It subsequently presents concealed attractors that lack any association with equilibrium. The chapter delineates hidden bifurcations and introduces a procient method for their detection, exemplied by a practical case. The nal chapter implements the proposed method on the Chua system, doing a numerical analysis and running simulations in MATLAB to corroborate the results. The chapter closes with the presentation and analysis of the acquired numerical results. |
| Sommaire : |
Dedicace 1 THANKS i Contents ii List of Figures 1 Introduction 2 1 Continuous Dynamic System 4 1.1 Introduction . . . . . . . . . . . . 4 1.2 Important De?nitions . . . . . . . . . 5 1.2.1 Phase Space . . . . . . . . . . . . 7 1.2.2 Attractors of Dissipative Systems . . . . . 8 1.2.3 Linearization of Dynamic Systems . . . . . . 10 1.3 Concept of Stability . . . . . . . . . . . . . 10 1.4 Bifurcation and Chaos . . . . . . . . . . . . 12 1.4.1 The Bifurcation Theory . . . . . . . . . 12 1.4.2 Chaos Theory . . . . . . . . . . . . . . . 14 2 Hidden Attractors and Hidden Bifurcations 17 2.1 Introduction . . . . . 17 2.2 Hidden attractors . . . . . . . . . 17 2.2.1 Analytical-Numerical Method for Hidden Attractor Localization . . . . . . . . . . . 20 2.2.2 Hidden Bifurcation . . . . . . . . . . . . 22 3 Application........... 23 3.1 Introduction . . . . . . . . . . . . . 23 3.2 Hidden Attractor for Chua's System . . . . . . . . . . . 23 3.3 Hidden Bifurcation in Chua's System . . . . . . . . . 29 3.3.1 Numerical Results . . . . . . . . . . . . . 31 Conclusion 34 Bibliography 35 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| MM/1366 | Mémoire master | bibliothèque sciences exactes | Consultable |
