Synchronisation des systèmes dynamiques chaotiques à dérivées fractionnaires.

Abstract

"The synchronization of two dynamic systems means that each system evolves following the behavior of the other. In mathematics, synchronizing two systems is to bring their trajectories until they end up being together, under the e¤ect of a coupling power exerted on the two systems. In this work we proposed a method of synchronizing two di¤erent chaotic systems of frac- tional order, this method is a generalization to the fractional order of the synchronization method by an ""auxiliary system "", based on the criterion of Routh -Hurwitz generalized to fractional systems, to ensure the stability of the error system. Where we obtained the necessary and su¢ cient conditions for complete the synchronization. We have shown the e¤ect of fractional order on synchronization which promotes the e¤ectiveness of this me- thod to distinguish the fractional case than the integer case and underline the importance of synchronization of fractional systems."