Function projective synchronization and parameter identification of different fractional-order hyper-chaotic systems

The function projective synchronization and parameter identification between the fractional-order chaotic system and hyper-chaotic system with uncertain parameters are researched, in which the fractional-order Chen chaotic system and the new fractional-order hyper-chaotic system are as examples. First, based on the fractional theory of stability and nonlinear dynamic theory, the nonlinear controller and parameter identification rules are designed. And by the nonlinear controller the function projective synchronization between the fractional-order 3D chaotic system and 4D hyper-chaotic system with uncertain parameters are realized. At the same time, the uncertain parameters are identified. Second, based on the fractional-order theory of stability the synchronization are proved strictly in mathematics. Finally, by the Predictor-Corrector scheme numerical simulation, the validity of the presented method is verified.