Synchronization of chaotic fractional-order systems via linear control

International Journal of Bifurcation and Chaos, Vol. 20(1), pp. 1-15 (2010)

Odibat Z., Corson N., Aziz-Alaoui M.A., Bertelle C.

Labo. of Applied Maths., EA 3821, Le Havre University, France.


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, Rossler and modified Chua systems. Numerical simulations are provided to verify the theoretical analysis.

Keywords: Chaos synchronization; fractional-order system; Caputo fractional derivative; Mittag-Leffler function; stability; linear control

Back to the previous page

Back to Aziz Alaoui's home page