Synchronization Control Between The Integer-order Chaotic Systems And Fractional-order Chaotic Systems

Synchronization control between the integer-order chaotic systems and fractional-order chaotic systems was focused on this article. Some approaches have been proposed to achieve chaos synchronization in fractional-order chaotic systems. Yet few of them have referred to the problem of synchronization control between the integer-order chaotic systems and fractional-order hyper chaotic systems. Recently, a lot of studies were concentrated on such relevant problems. It is clear that compared to previous research study, the synchronization of fractional-order hyper chaotic systems and integer-order chaotic systems could be more complex and broader. Using projective synchronization and complete synchronization methods to achieve synchronization in fractional-order chaotic systems and the integer-order chaotic systems. By designing a fuzzy controller and a tracking controller, we sought to achieve the synchronization of the fractional-order hyper chaotic system and integer-order chaotic systems.(1) The history, characteristics and principles of chaos were introduced in this chapter. Systematic review was presented of chaotic synchronization and its application. Fractional definitions, nature and value were introduced. According to research on the status of synchronization of chaotic systems research at home and abroad, analyzes the advantages and disadvantages of the acquired results.(2) A new fractional-order hyper chaotic system was proposed and its dynamic behavior was discussed. It had been verified that this system was a fractional-order hyper chaotic system. Based on the stability theory of fractional-order systems and tracking control, a nonlinear controller is proposed to accomplish this synchronization between the integer-order chaotic system and fractional-order chaotic system. Furthermore, example is presented to illustrate the effectiveness of the proposed scheme, which is the synchronization between fractional-order chaotic system and integer-order chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.(3) In this paper, a new fractional-order hyper chaotic system was proposed and its dynamic behavior was analyzed. It had been verified that this system was a fractional-order hyper chaotic system. Using fuzzy control technology to control the chaos systems, the feedback linearization restrictions of traditional method on parameters could be overcome. T-S fuzzy model could be a better approach in chaotic system than others. By designing a T-S fuzzy controller and choosing proper control parameters, the drive and response systems are synchronized. And its feasibility through simulation algorithms and numerical analysis was verified.(4) The principle and significance of secure communication was introduced. Synchronization between the integer-order chaotic systems and fractional-order chaotic systems for secure communication is researched. Its feasibility was verified through simulation algorithms and numerical analysis.