WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Chaos Control and Synchronization of a Fractional-Order Autonomous System
Authors: ,
Abstract: Liu, Liu, and Liu, in the paper “A novel three-dimensional autonomous chaos system, Chaos, Solitons and Fractals. 39 (2009) 1950-1958”, introduce a novel three-dimensional autonomous chaotic system. In this paper, the fractional-order case is considered. The lowest order for the system to remain chaotic is found via numerical simulation. Stability analysis of the fractional-order system is studied using the fractional Routh-Hurwitz criteria. Furthermore, the fractional Routh-Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilibria. Based on the fractional Routh-Hurwitz conditions and using specific choice of linear controllers, it is shown that the fractionalorder autonomous system can be controlled to its equilibrium points. In addition, the synchronization of the fractional-order system and the fractional-order Liu system is studied using active control technique. Numerical results show the effectiveness of the theoretical analysis.