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Active Sliding Mode for Synchronization between A Fractional-order Chaos and Integer-order Liu System

Rui-xin Wang, Bin Wang, Yuan-gui Zhou, Wei-yu Wang

Abstract


A new four-dimensional (4-D) fractional-order chaotic system is proposed in this paper. Theoretically, a necessary condition for occurrence of chaos is obtained. Numerical investigations on the dynamics of this system have been carried out. It is shown that in case of commensurate system the lowest order of the new fractional-order system to yield chaos is 0.83, and a list of state trajectories is presented with fractional derivative of different areas. Furthermore, based on the fractional stability theory, a new active sliding mode control (ASMC) approach is proposed to realize the chaos synchronization between the fractional-order system and integer-order Liu system. Finally, simulation results are given to demonstrate the effectiveness of the proposed active sliding mode control method. The synchronization process is a smooth transition, and the transition time is very short.

Keywords


fractional-order system, integer-order system, chaos synchronization, active sliding mode control.

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