Research On Problem Of Several Chaotic Synchronizations

The research on nonlinear dynamics not only has significance of science,but also has good banausic prospects.It has been getting along well with theory and application.Chaos is one of the core of nonlinear dynamics,and the great valueness and good prospects of chaos synchronization in engineering and technology,military and other areas is a hot spot of nonlinear science research at all times.In the paper,a brief introduction to historical backgrond,research progress and typical methods about chaos,chaotic control and synchronization is given firstly.Then this dissertation is devoted to the study on synchronization for a class of chaotic systems.The research includes chaotic synchronization of a class of chaotic systems based on nonlinear control, projective synchronizdtion for a hyper-chaotic systems with unknown parameters,specific linear generalized synchronization for a class of chaotic system with unknown parameters and chaos synchronization induced by sliding-mode control for unified chaotic system with parameter mismatches..The research focuses mainly on the followings:(1),A class of chaotic systems is extracted from Lorenz system and so on.Based on Lyapunov stability theory,a nonlinear controller is designed for the complete synchronization of the coupled chaotic systems.(2),On the basis of theory of complete synchronization,projective synchronization is studyed based on adaptive control.For the new chaotic system,the nonlinear control and the adaptive principle of parameters make the master-slave system projective genearlized synchronization under the condition of uncertain parameters.By the Lyapunov stability theory, we prove that the theory of the chaotic system is right.(3),Linear generalized synchronization for a class of chaotic system with unknown parameters is investigated.For the class of chaotic systems,on the basis of the correlation between linearly generalized function and coefficient matrix of the drive system's linear segment,the linear control and the adaptive principle of parameters make the drive-response system linear genearlized synchronization under the condition of uncertain parameters.By the Lyapunov stability theory and Barbalat lemma,the theory of the chaotic system proves to be right.For concrete chaotic systems,the controller is able to be simpler.(4),Using the sliding mode control technique,a new adaptive control law is established which realized the synchronization of two unified chaotic systems with parameter mismatches.Both theoretical analysis and simulation have been presented to verify the validity of the developed control scheme.For all theoretical results,we proposes numerical simulations which illustrates the corresponding theoretical results.