Chaos in the Fractional-Order Qi System and Its Synchronization Using Active Control

In this paper, the dynamics of the fractional-order Qi system is studied. By utilizing the fractional calculus theory and computer simulations, it is found that chaos exists in the fractional-order Qi system with order less than 3. The lowest order to yield chaos in this system is 2.745. Based on the stability theory of the fractional-order system, chaos synchronization of the fractional-order Qi system and the fractional-order Chen system, is achieved using the active control technique. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.