Fractional Order Hyperchaotic System And Its Synchronization Image Encryption Applications

Nonlinear systems exist in most of the natural and social phenomena, its rich variety of complex movement patterns and process play a significant role on our understanding of the objective world. As an important branch of nonlinear science, chaos reveals the widespread nature and human society complexity. It is said that the international chaos following the advent of relativity and quantum mechanics in the 20th century, is third revolution the human understanding and transforming of the world. With the deepening of the chaotic, hyperchaotic system has been developed as one of the new discipline. Compared with the general chaotic system, hyperchaotic system has a more complex dynamic behavior, and its randomness and unpredictability are greatly enhanced. Therefore, hyperchaotic system is more extensively valuable in engineering applications.In many cases, chaos phenomenon is not expected. For instance, in some complex industrial process, the unpredictable disturbance by which some Chaotic dynamics are often showed are filtered out by statistical methods in the past, however, with in-depth understanding of chaos, people gradually realized that, because this phenomenon of the disturbance can not be ignored, it is necessary to study how to control the chaos. The sensitivity of chaotic systems on initial makes Synchronization of chaos to be the key to the nonlinear study. The method of chaos control and synchronization with its application is just a prologue, which is mutual penetrated with of many other disciplines to become a major subject area of nonlinear research focus.In the past, the study of chaos is mostly aimed at integer-order chaotic system. In recent years, fractional differential operator is introduced into the chaotic system. There are more complex dynamics of chaotic behavior in fractional order system than in the integer order system, also fractional order system can reflect physical phenomena better than integer-order chaotic system. So the fractional power system control and synchronization of chaos has indispensable practical value is becoming the focus of research, and this is the main content of this thesis.With computers and the growing of various communication networks, information security requirements become increasingly important. Since chaos synchronization was proposed by Pecora and Carroll, that chaotic sequences is used for secure communication is started, and the Development of the chaos synchronization theory has made it to be widely applied in secure communication. Compared to normal chaos, more unpredictable and complex dynamic the chaotic behavior is, more prospects it has in secure communication applications.In this thesis, firstly, the chaotic system definition, characteristics and development process are given, and the chaotic synchronization methods and calculus is described.Secondly, the fractional dynamics of hyper-chaotic systems which are proposed in the thesis are analyzed and experimental validated systematically. Thirdly, the fractional hyper-chaotic synchronization method which is studied are outlined, and adaptive control and tracking control of two synchronization methods are used for achieving the synchronization control between their different structure; At last, applications and methods of the chaos synchronization in secure communication are discussed, and fractional-order hyper-chaotic synchronization are used in digital image encryption and decryption.