The Synchronization Study Of Hyper-chaotic System With Uncertain Parameters

In this paper, the synchronization of hyper-chaotic system with uncertain parameters isinvestigated. The five-dimensional Rossler system is selected as the typical system to study.This paper is on the basic of the theoretical analysis. The numerical simulation is proved byMatlab, and the chaotic electronic circuit is designed to achieve the synchronization ofhyper-chaotic system.Firstly, the five-dimensional Rossler system is researched by the theoretical analysis; theelectronic circuit is designed and constructed to realize the dynamic behavior of thehyper-chaotic system. The synchronization problem of uncertain hyper-chaotic Rosslersystem is finished mainly by linearity feedback method, nonlinearity feedback method, scalarcontrol method, and adaptive control method.Secondly, it is studied about the generalized synchronization problem offive-dimensional Rossler system with same orders and different orders hyper-chaotic systems,which is achieved by nonlinearity feedback method and adaptive control method. Based onthe Lyapunov theory, we design the appropriate controller and the update laws of parameters,but the controller of generalized synchronization is complex for the different orders systems.Finally, hybrid synchronization and dislocated synchronization are combined effectively.The hybrid-dislocated synchronization is investigated for the uncertain hyper-chaotic systems.On the basic of the theoretical analysis, the numerical simulation and electronic circuit areproved to verify the effectiveness of the designed controllers and update laws of parameters.In conclusion, it is investigated about the synchronization problem of hyper-chaoticsystem, the experiment evidence and the relative theoretical analysis are provided for theapplications of secure communications, so it is practically significant.