Chaos et synchronisation (généralisé) dans les systèmes dynamiques.

Abstract

In recent years, chaos synchronization has been widely explored and studied because of its potential applications, such as in secure communication, chemical reactions, biological systems, information science. Thereby, a variety of approaches have been proposed for the synchronization of chaotic systems, such as complete synchronization, generalized synchronization and projective synchronization. Recently, hybrid function projective synchronization (HFPS) for chaotic systems is extensively considered. On the other hand, studying the inverse problem of this scheme with produce, a new synchronization type called Inverse Hybrid Function Projective Synchronization (IHFPS), is an attractive and important idea. So, we introduce in this thesis the IHFPS for 5-D general class of chaotic systems in continuous-time. To achieve IHFPS, we use the lyapunov stability theory. More recently, new research has focused on studying the combination of several types of synchronization. Therefore, at the Örst, we constructed a new type of hybrid chaos synchronization based on the on coexistence of Generalized Synchronization (GS) and its inverse (IGS). By using Lyapunov stability theory and stability theory of linear continuous-time, some su¢ cient conditions are derived to prove the existence of (GS) and (IGS) between 3-D master system and 4-D slave hyperchaotic system in 3D and 4D, respectively. Secondly, we illustrate new schemes which prove the existence of the Full State Hybrid Function Projective Synchronization (FSHFPS) and its inverse (IFSHFPS) between a 3-D master system and a 4-D salve system in 4D and 3D, respectively. Some examples with numerical simulations allowed us to verify the e§ectiveness of the theoretical analyzes developed herein.