Adaptive Synchronization Of Fractional Order Chaotic Systems And Application In Secure Communication

Chaos,a kind of overall stability and local random motion, is a combination of determinacy and randomization. As a complicated phenomenon existed in the nature, chaos control has obvious characteristics in sensibility about initial value, wide spectrum and internal randomness. It is a specific movement style between random movement and certain movement, and has a great application value and development potentials.Fractional calculus can objectively reveal and describe the physical characteristics of the actual system compared to the integer order calculus. The fractional order chaotic system with its unique advantages shows the unique charm and huge development potential in secure communications and other applications. Chaos synchronization of fractional order system, the key technology of secure communication technology, has become a hot topic in scientific community. Therefore, the article will deeply study chaotic synchronization of fractional order systems and explore its application in secure communication base on the theory of fractional calculus, the main content as follows:① The paper studied the dynamical behavior of fractional modified Liu chaotic system. First of all, the mathematical model of the system was converted into dynamic simulation model by the predictor corrector method. Secondly, the fractional order circuit structure of the system is built using time and frequency domain transform method. And through the dynamic simulation and circuit experiment results of fractional order Liu system proved that the system can exhibit chaotic behavior in specific parameters.② In view of dislocated projective synchronization for fractional-order chaotic systems, an active controller is investigated base on control strategy of dislocation projection. And analyze the stableness of fractional order system by the stability interval and the pole placement method.③ The synchronization for a class of fractional order chaotic systems with uncertain parameters and random disturbances is investigated. The uncertain parameters are identified online. Based on the stability theory of the fractional order Mittag-Leffler, an adaptive controller is designed for the fractional order chaotic systems with unknown parameters. The adaptive tracking method is used to solve the noise and other interference of system. The Adaptive robust controller not only can realize the chaotic synchronization, but also can identify parameters and overcome disturbances.④ Signal distortion, loss and other problems exist in the communication process. Chaos masking communication scheme are given based on chaotic masking and improved chaos masking, which not only consider the parameters of encryption and decryption system loss, also take into account the interferences in the channel, the more closer to the real situation. Through the simulation, the paper further illustrates the effect of secret communication scheme.