Research On Fractional Order Chaotic Systems And Their Synchronization Control

The study on fractional order calculus theory has a history more than 300 years, however, the scholars studying on fractional order calculus theory mainly exist in the field of math during the past long period. In1983, Mandelbort initially suggested that there are plenty of fractal dimension phenomena in the field of nature and the field of science and technology, and there are self-similarities between integer and fraction. Then, as the dynamics foundation of geometry and fractal dimension, fractional order calculus gained new development and become a hot issue of the international. The synchronization control of fractional order system is the focus of recent researches, but chaotic synchronization methods are limited. It is believed that the chaos synchronization will play an important role in fields such as secure communication in the future.In this paper, fractional order chaotic systems and their synchronization are studied by numerical simulation. The main contents can be divided into six parts: The first part, the development process of chaos, the characteristics of chaos and the road leading to chaos are introduced. The development of fractional order chaos systems and their synchronization are investigated at home and abroad, the results achieved and the existing shortcomings are summarized. In the second part, the numerical simulation methods for fractional order chaos system are given. In the thirdly part, based on the nonlinear observer and stability theory of fractional order systems, a class of fractional synchronization of chaotic systems state observer are designed, has been such a state can not be fully measured fractional order chaotic systems synchronization program. In the fourth part, a new fractional order chaos system is invesgated. Based on the stability theory of fractional order systems, we analyse stability condition for chaos to exist in the commensurate and incommensurate new fractional order system respectively. At last, based on active control method and observe-based control method, two identical new fractional order chaotic systems achieve synchronization respectively. In the fifth part, a new fractional order hyperchaos system is studied. We analyse the dynamics behavior of the commensurate and incommensurate new fractional order hyperchaotic system respectively, followed by the use of active feedback control, two identical new fractional order hyperchaotic systems and nonidentical new fractional order hyperchaotic systems achieve synchronization. In the sixth part, the model of integer-order simple interconnected power system and the bifurcation of the chaotic status are introducted, and then based on fractional order theory, the model of fractional order interconnected power system is analysed by numerical simulation. Finally, based on nonlinear feedback control and active feedback control method, we realize the synchronization control for the fractional order interconnected power system chaotic oscillation respectively.