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

Since the applications in the field of secure communication and so on, the synchronization of fractional-order chaotic system catches many attentions and is researched extensively. In this paper, we launch of a series of research on fractional-order hyperchaotic synchronization by the method of combing theory prove and numerical simulations. The main work of the paper is summarized as follows.(1) The impulsive synchronization scheme of fractional-order hyperchaotic systems is studied. We get the sufficient conditions of integer-order hyperchaotic system s synchronization through theory analysis, and apply this condition to fractional-order hyperchaotic systems. Numerical simulation results further demonstrate the effectiveness and feasibility of this scheme. Many experimental results indicate this scheme has universaliy to fractional-order hyperchaotic systems.(2) Based on projective synchronization theory, a proper response system of fractional-order system is designed, the synchronization sufficient conditions of the dive system and response system is obtained based on the fractional-order stability theory. The modified projective synchronization is realized through transferring one variable to response system from drive system. Furthermore, a controller is designed to realize the modified projective synchronization of two determained fractional-order hyperchaotic systems. This synchronization schmeme reduce the information need to be transferred in order to realize chaotic synchronization, and expand the applicarion range of projective synchronization.(3) A robust synchronization scheme of factional-order hyperchaotic systems is promoted. Trough theory analysis, we get that the synchronization error can be forced and kept inside a ball around the origin when the drive system and response system both have external noises, and the radius of the ball can be chosen by designing proper controller.(4) The generialized synchronization methods of hyperchaotic systems is investigated base on Lyapunov stable theory, and the generialized synchronization of integer-order hyperchaotic system is realized. The synchronization condition is applied to fractional-order hyperchaotic systems, and the linear and nonlinear synchronizatioin is achieved.