| Chaos widely exists in natural and social, which is a special and complex nonlinear system which has universally application prospects in the economic, biology, physics and other fields, especially in security of communication.Recently, the fractional calculus quickly becomes the focus of research which has many advantages compared with the integer order calculus, such as a clearer physical significance, a more simple description and explanation of the problem and closer to mathematical model of the actual system. The control and synchronization problems of the fractional order chaotic systems are mainly studies in this paper, and the secure communication of image data is realized at last. The main work of this paper is summarized as follows:1. Firstly, the background, development, types and methods of synchronization, applications of chaotic systems are briefly introduced. The basic concepts of fractional order systems are introduced, including the definition of fractional order system, the stability theory of fractional order system and numerical simulation theory of fractional calculus.2. Synchronization control of fractional order chaotic systems is studied based on the fractional order Lorenz system. Four synchronization control strategies are proposed by using the methods of the state feedback control and passive control from the angle of the simplified controller. The numerical simulations are realized on the simulation software. Finally, advantages and disadvantages of design methods are compared. The influence of synchronization time and synchronization effect is analyzed through the selection of parameters. The influence of synchronization effect is discussed by different synchronization methods.3. Adaptive synchronization control of fractional order chaotic systems is researched based on the fractional order Lorenz system and the fractional order unified chaotic system. The corresponding adaptive controller and adaptive laws are constructed by using the special matrix configuration method and passive synchronization control method to realize the system synchronization and parameter estimation in the case of the unknown parameters. Finally, numerical simulations are implemented in a simulation software. The effectiveness of the methods is verified by the simulation diagram.4. The secure transmission of image data is studied. Image encryption is realized by adding the chaotic sequence which is produced by the synchronization between fractional order chaotic systems. The encrypted image has a good safety performance under the display of histogram and pixels of correlation coefficient. At the same time, the research of color image encryption and decryption cleverly solved through the decomposition of three primary colors. |
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