| Fractional chaotic dynamical systems have richer and more complex dynamics behaviors than that of integer-order systems, and the advantages of enhanced randomness and unpredictability. In recent years, systems which based on fractional differential and integral fractional, have been researched extensively, involving fractional circuit, fractional digital signal processing, fractional dynamics control systems and fractional-Chaos and super-chaos, Chaos Control and fractional chaos synchronization, and security communications. And a lot of theoretical and practical results are obtained. In this thesis, based on the famous Chua's circuit system the characteristics of fractional chaotic dynamical systems is analyzed, and several important issues have been delved into. The main contents of this thesis are as follows:â‘ Research on chaos of fractional chaotic dynamics systemsFirstly, the integer-order Chua's circuit system is transformed into fractional one, and then by using fractional time-domain solution and iterative thinking, a new solution for fractional system is constructed. With the Matlab software platform, a simulation of a model based on fractional Chua's circuit system is done, and the parameter values which chaos would occur is obtained. And the picture of the fractional Chua's circuit system chaotic attractor is illustrated.â‘¡Research on synchronization of fractional chaotic dynamics systemsResearch of synchronization of chaotic systems is one project of the most important application research, and has very important theoretical and practical value. Although integral order chaotic dynamical systems had been more deeply studied, people invented many of good synchronization modes. However, these models can not be applied completely to fractional dynamics system. In this dissertation, the fractional synchronization model presented by C. P. Li is studied, and its inadequacies in the theory is analyzed, and the corresponding bifurcation diagram and synchronization error map have been given. Finally the one-way synchronization mode is studied deeply. Comparing the three situations with coupling matrix of (k, 0, 0), (k, k, 0), (k, k, k) in aspects of the convergence rate, error, and so on, the result comes to that the performance is the best with matrix (k, k, k) as coupling matrix. This analysis method can be extended to other analysis of fractional chaotic synchronization model. â‘¢Application of fractional chaotic dynamics system in security communicationSecurity Communication is one of the most common applications in chaotic study. Chaos synchronization is the foundation and prerequisite to communication, is also the key to that a communication is successful or not. Therefore, the synchronization mode with the best performance is selected to make sure information is received completely, and to protect the confidentiality and integrity of the information. In order to verify the correctness of the method, a computer simulation has been processed and the simulation results are the same with theoretical analysis.
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