Research On Control And Different Structure Synchronization Of Fractional-order Chaotic Systems

Chaos, a kind of nonlinear motion form widely existing in nature, has quickly become the focus of scholars study and discussion because of its broad application prospects. The control and synchronization of chaos is the key of applying chaos in practice, and also the focus of attention currently. The rise of the theory of fractional calculus broaden the depth and breadth of chaos control and synchronization. Research on control, synchronization and the application of the fractional order chaotic systems is still in the initial stage, although the chaos control and synchronization have more mature theory. Therefore, it has become the most advanced academic hot spot in the 21 st Century. In this paper, we mainly studied the control and different structure synchronization of fractional order chaotic and hyperchaotic systems. The main contents and results are as follows:Firstly, a new fractional order chaotic system and a fractional order hyperchaotic system are analyzed.The fractional-order chaotic system is controlled by optimized feedback controller. The effectiveness is verified by theoretical analysis and numerical simulation. The fractional-order hyperchaotic system has been controlled and the unknown parameters have been recognized by the modified adaptive control method. The feasibility of this control method is verified by numerical simulation. Compared the effects of the chaos control with unknown parameters using feedback control and the original adaptive control method, it is concluded that the modified adaptive control method has the faster speed and the higher efficiency.Secondly, for different structure synchronization of fractional-order hyperchaotic system with uncertain parameters, the adaptive control method is introduced. Different fractionalorder hyperchaotic systems with uncertain parameters are synchronized by the corresponding synchronization schemes for the actual systems. The simulations are carried out using general synchronization and the adaptive synchronization method. One is to verify the validity of the method proposed in theory. And the other one is that the proposed method could realize the identification of unknown parameters, and have more advantages than the general synchronization method in the synchronization of fractional order hyperchaotic system with uncertain parameters.Lastly, different fractional-order chaotic systems with different dimensions are synchronized by the synchronization scheme and controllers based on the idea of projective synchronization. An example is cited to achieve the synchronization between two different dimensions fractional-order chaotic systems, and being used numerical simulation to verified it. Moreover, combining it with secure communication. An example is selected to simulate and verify the effectiveness of the proposed communication scheme to the information security transmission.