Chaos in fractional-order Liu system and a fractional-order unified system and the synchronization between them

This paper studies the chaotic behaviors of the fractional-order Liu system and the fractional-order unified system which were presented several years ago. It is found that chaos exists in the both systems with order less than three and the lowest order to have chaos is 0.3. The calculation results of the maximum Lyapunov exponents when the system is chaotic illustrate the existence of chaos. Chaos synchronization between fractional-order Liu system, fractional-order Lorenz system and fractional-order Lu sytem is realized by employing active control technique. Theoretieal analysis and numerical simulations demonstrate the effectiveness of the proposed method..