Study Of Synchronization Control For Fractional Order Chaotic Systems

It is well known that the problem of synchronization control for fractional orderchaotic systems is an important problem in nonlinear science, and its research resultshave been extensively applied in many diferent areas, and especially, it has importantsignifcance in the data encryption, communication security and radar signal etc. however,along with the Progress and development of the society, we need to study the synchroniza-tion of the chaotic systems more detailed. In this paper, based on the stability theory, byconstructing the diferent controllers, complete synchronization of fractional order Voltachaotic systems, quasi-synchronization of diferent fractional-order chaotic systems withexternal perturbations and modifed projective synchronization of fractional order hyper-chaotic systems are realized, respectively.The main contents in this paper can be summarized as follows:The frst chapter, the research background of chaos and chaos control and the re-search status of fractional order chaos and chaos control are introduced. After that, theorganization of this paper is given.The second chapter, the defnition of fractional order derivative, the concept of allkinds of synchronization and fractional order system stability theorem are introduced. Tolay the foundation for the back of the theoretical analysis.The third chapter, chaotic dynamics characteristics of fractional order Volta systemis simply introduced, and according to the stability theorem of fractional order linear sys-tems, the corresponding controller is designed to realize complete synchronization for thefractional order Volta chaotic systems. Numerical simulation verify the synchronizationscheme is correct and efective.The fourth chapter, based on the fractional order Comparison principle, the controlmethod of quasi-synchronization of diferent fractional-order chaotic systems with external perturbations is given. And by applying this method to achieve quasi-synchronizationbetween fractional-order Lorenz chaotic systems and Chen chaotic systems with externalperturbations. Theoretic proof and numerical simulation verify the efectiveness andcorrectness of proposed method.The ffth chapter, frstly, fractional order Ro¨ssler hyperchaotic systems and fractionalorder Chen hyperchaotic is introduced. Then in view of stability theory of fractional ordersystem, through designing the suitable controller to realize modifed projective synchro-nization of fractional order Ro¨ssler hyperchaotic systems and modifed projective synchro-nization between fractional order Ro¨ssler hyperchaotic system and fractional order Chenhyperchaotic system, respectively. In the end, Theoretic proof and numerical simulationshow the efectiveness and correctness of given method.