Synchronization And Control Of Several Kinds Of Typical Fractional-Order Chaotic Systems

At present, it is known that some fractional-order differential systems behave chaotically, and fractional-order systems have attracted more and more people's interest, there are two problems considered, the first problem is when an ordinary differential equation system is chaotic, under what condition the corresponding fractional-order system is also chaotic. More exactly, for what orders, the fractional-order system is chaotic. The second is that given a chaotic fractional-order differential system, how to design a scheme such that synchronization of many such systems is achieved. In this thesis, the relative problems of synchronization and control of several kinds of typical fractional-order chaotic systems are studied using the methods of theoretical derivation and numerical simulation.The main achievements contained in the research are as follows:Firstly, by utilizing the fractional calculus techniques and the largest Lyapunov exponent method, studies the problem of chaotic behaviors and synchronization of the fractional-order two-disk dynamo system, designs the active controllers, and then proves that the self-synchronization of the fractional-order two-disk dynamo system, and the fractional-order two-disk dynamo system's different structure synchronization with the fractional-order Lorenz system can both arrive by using the theoretical analysis and numerical simulations.Secondly, studies the projective synchronization of the fractional-order unified system. Based on the stability theory of fractional-order systems and the pole placement technique, designs a synchronization scheme with the state observer method and achieves the projective synchronization of the fractional-order chaotic unified system. The form of the proposed scheme is simple and can be easily implemented. It is robust and is able to realize the projective synchronization in a general class of fractional-order chaotic systems without the limitation of partial-linearity.Lastly, designs a generalized synchronization scheme based on the stability theory of fractional-order systems and the pole placement technique, the condition of the drive-response systems' generalized synchronization is obtained theoretically and analytically, and achieves the generalized synchronization of two different fractional-order chaotic systems. The synchronization method is adopted to realize the generalized synchronization of three illustrative examples, such as the fractional-order Chen system and the fractional-order R(o|¨)ssler system, the fractional-order Lüsystem and the fractional-order hyperchaotic Lorenz system, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system, and the numerical simulation results verify the effectiveness.