Sur la synchronisation de systèmes chaotiques bidirectionnellement couplés

Laurent Laval (1) , Jean-Pierre Barbot (2, 1) , Christophe Letellier (3)

1 ECS-Lab - Électronique et Commande des Systèmes Laboratoire
2 NON-A - Non-Asymptotic estimation for online systems
3 CORIA - Complexe de recherche interprofessionnel en aérothermochimie

Considering two chaotic Rossler systems, this paper presents a study on the forced synchronization of two systems, bidirectionally coupled by transmitting unidirectionnal signals which explicitly depend on a single state variable (from the emitter) and only affect directly the dynamics corresponding to the transmitted state variable (of the receiver). According to an analysis based on the control theory, we exhibit that (partial or complete) synchronization mainly depends on conditions about the stabilisability of variations between the trajectories of the two systems. Morevover, we point out that, even if it is effective, complete synchronization can not, from a theoretical point of view, be absolutly guaranteed for all time t, as it explicitly depends on the domain of the (bounded) space in which the trajectories of systems mostly evolve.

Domaines: Systèmes dynamiques [math.DS]

Laurent Laval, Jean-Pierre Barbot, Christophe Letellier. Sur la synchronisation de systèmes chaotiques bidirectionnellement couplés. Rencontre du Non-Linéaire 2013, Mar 2013, Paris, France. ⟨hal-00923671⟩