Adaptive synchronization of fractional order chaotic systems based on modified feedback approach

In this paper, a modified adaptive feedback control scheme is introduced to ensure synchronization of two different fractional order chaotic systems with unknown parameters and different fractional orders. Based on the stability of fractional order system, a modified adaptive controller and an update law of parameters are developed. The proposed scheme is global and theoretically rigorous. One example is given to illustrate effectiveness of this method, in which the synchronization between fractional order Chen system and fractional order Qi system is successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.