Study On Synchronization Of Modified Fractional-order Liu Hyperchaotic System

In this paper, the synchronization of fractional-order modified Liu hyperchaotic system is investigated mainly. Three kinds of classical methods of synchronization of chaotic systems(feedback synchronization, projective synchronization, adaptive synchronization) are utilized to study the synchronization of fractional-order modified Liu hyperchaotic system. Theoretical analysis will be the basis of this paper, meanwhile numerical emulation and circuit simulation are used to verify these studies.First of all, this paper briefly describes the current status of synchronization for the fractional-order chaotic systems, and summarizes the studying meaning of this paper. We propose the fractional-order modified Liu hyperchaotic system, and then use theoretical analysis to make sure this system is hyperchaotic system. Finally, numerical emulation and circuit simulation of this system are given to show that this system has complex dynamical behavior. All of these are done to prove help for the following work.Secondly, this paper does studies on synchronization of fractional-order modified Liu hyperchaotic with projective synchronization method, feedback synchronization method and adaptive synchronization method. In the first place, suitable controllers are created based on fractional stability theory, which realizes the linear feedback synchronization and nonlinear feedback synchronization of fractional-order modified Liu hyperchaotic system. Later, by choosing right controllers, generalized projective synchronization and modified projective synchronization of fractional-order modified Liu hyperchaotic system come true. Finally, we design feedback adaptive synchronization controller of fractional-order modified Liu hyperchaotic system and update laws based on Lyapunov function determining fractional system steady, and accomplish the adaptive synchronization of system. Numerical emulation and circuit simulation illustrate that these synchronization methods are effective to fractional-order hyperchaotic system.Finally, Synchronization of fractional-order modified Liu hyperchaotic system is realized through feedback synchronization method, function projective synchronization method and adaptive synchronization method by connecting fractional stability theory, while the unknown parameters are identified by connecting the fractional stability theory, in the end, numerical emulation also proves that these synchronization methods can be applied to fractional-order hyperchaotic system.