On chaos control and synchronization of the commensurate fractional order Liu system. (English) Zbl 1261.35148

Hegazi, A. S.; Ahmed, E.; Matouk, A. E.

Commun. Nonlinear Sci. Numer. Simul. 18, No. 5, 1193-1202 (2013).

Summary: In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate fractional order Liu systems are investigated. We also obtain the necessary condition for the existence of chaotic attractors in the commensurate fractional order Liu system. The effect of fractional order on chaos control of this system is revealed by showing that the commensurate fractional order Liu system is controllable just in the fractional order case when using a specific choice of controllers. Moreover, we achieve chaos synchronization between the commensurate fractional order Liu system and its integer order counterpart via function projective synchronization. Numerical simulations are used to verify the analytical results.

MSC:

35R11	Fractional partial differential equations
35B35	Stability in context of PDEs
35Q93	PDEs in connection with control and optimization

Keywords:

commensurate fractional order Liu system; stability conditions; chaos; chaos control; projective synchronization