Fractional Chaotic System Synchronization And Its Application In Secure Communication

A chaotic system is a nonlinear deterministic system that shows unpredictable and complex behavior. The sensitivity to the initial conditions is the prominent characteristics of chaotic systems, and this makes the methods of chaos synchronization being widely applied in the field of secure communication. Recently, chaos synchronization has been an active research of the nonlinear subject. This new technology promises to have a significant impact on many novel engineering applications. The challenging research field has become a scientific inter-discipline involving many other fields. As fractional order chaos has more complex characteristics than the integer order counterpart in areas such as secure communication with potential applications, so it is more worthy to study the fractional order chaos.This thesis combines theoretical derivation and numerical simulation method to research some kinds of fractional-order Volta's System synchronization problems and their applications in secure communication. The main contributions are listed as follows:1. Studies chaos synchronization of fractional-order Volta's system via active control. Based on the method combining feedback control and active control, the control law is presented to achieve chaos synchronization. Simulation results for identical fractional-order Volta's system and different fractional-order Volta—Newton-Leipnik chaotic systems are presented to demonstrate the effectiveness and feasibility of the proposed method.2. Studies chaos synchronization of fractional-order Volta's system via projective control. Based on active sliding mode theory to synchronize chaotic fractional-order systems, the control law is presented to achieve chaos synchronization, and the stability of the proposed method is analyzed. Simulation results for identical fractional-order Volta's system and different fractional-order Volta—Liu chaotic systems are presented to demonstrate the effectiveness and feasibility of the proposed method.3. Studies chaos synchronization of fractional-order Volta's system via adaptive hybrid projective synchronization control. Based on the fractional stability theory, the controller and recognizing rules of the uncertain parameters are designed. Tracking control and synchronization of fractional-order Volta's system are realized. Simulation results for identical fractional-order Volta's system and different fractional-order Volta—Lu chaotic systems are presented to demonstrate the effectiveness and feasibility of the proposed controller and recognizing rules of the uncertain parameters.4. Studies the chaotic applications in secure communication. Based on chaos synchronization of fractional-order Volta's system via projective synchronization control, a chaotic masking secure communication scheme is designed by encryption function. Numerical simulation results are presented to demonstrate the effectiveness and feasibility of the proposed scheme.