Synchronization of chaotic fractional-order systems via linear control

Zaid M. Odibat (1) , Nathalie Corson (2) , Moulay Aziz-Alaoui (2) , Cyrille Bertelle (3)

1 ULH - Université Le Havre Normandie
2 LMAH - Laboratoire de Mathématiques Appliquées du Havre
3 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear fractional-order systems, sufficient conditions for chaos synchronization of these systems are given. Control laws are derived analytically to achieve synchronization of the chaotic fractional-order Chen, Rössler and modified Chua systems. Numerical simulations are provided to verify the theoretical analysis

Mots clés: Chaos synchronization; Fractional-order system; Caputo fractional derivative; Mittag-Leffler function; Stability; Linear control

Domaines: Complexité [cs.CC]; Dynamique Chaotique [nlin.CD]

Zaid M. Odibat, Nathalie Corson, Moulay Aziz-Alaoui, Cyrille Bertelle. Synchronization of chaotic fractional-order systems via linear control. International journal of bifurcation and chaos in applied sciences and engineering , 2010, 20 (1), pp.1-15. ⟨hal-00430513⟩