Function Projection Synchronization Of Fractional Order Chaotic Systems Theoretical Study

In recent years, due to the nonlinear science the rapid discovery of, The researchers found that chaotic synchronization phenomenon is more and more common in our life, It is mainly used in secret communication, biology, physics, and the application of chaotic synchronization field continues to expand. Due to the tremendous potential applications in the chaotic synchronization, it has been a focus in the study of chaos theory.Function projective synchronization is change the scaling factor in projective synchronization to proportion function, namely the state of the drive system and response system according to the given the ratio of function to achieve synchronization. Because the ratio function are unpredictable, so it makes the existence of chaos system is more complex, has improved the security of the system.Therefore, the function projective synchronization in secure communications has important application value.So far, the study of chaotic systems are mostly based on integer order differential and integral calculus equation. But compared with integer order differential equation,the fractional order differential equation system can be more accurate description of the nature. Due to the present stage for the research achievements of fractional order chaotic systems is relatively less, and the study of fractional order chaos theory is more broad application prospects. Therefore, study of fractional order chaotic system synchronization function projection has important theoretical value.In this paper, the main content is as follows:On the basis of the theory of fractional order chaotic systems stability and function definition of projective synchronization, According to the given drive system and response system state equation, Design the controller to achieve synchronization function projection drive system and response. We selected the same drive system and response system of the structure of the chaos systems and chaoticsystems with different structure.Based on the forecast correction method, the use of Matlab to prove the validity of the controller design.In the presence of time delay of the drive system and response system, on the basis of the theory of fractional order chaotic systems stability and hysteresis function projective synchronization, the definition of design controller makes the time delay of the drive system and response function projective synchronization.Respectively by choosing the same structure of the chaotic systems and chaotic systems with different structure, the corresponding controller is designed,finally the correctness of the test controller design by Matlab.