Research On Chaos Control And Synchronization In Real And Complex Systems

Chaos is a unique form of motion of nonlinear dynamical systems,and it is widely used in nature.In recent years,with the rapid development of the field of chaos,chaos control and synchronization have penetrated into many other fields,and have very important research value and application prospect in engineering technology,and cause great concern of the dynamics and control engineering experts and scholars,it becomes one of the hot issues in the field of nonlinear science.In this paper,the chaos control and synchronization problems of real chaotic systems and complex chaotic systems are deedy studied by theoretical derivation and numerical simulation.Specific work is summarized as follows:Firstly,for a three dimensional autonomous real chaotic system,the dynamic behavior is studied.And based on Lyapunov stability theory,linear controller and nonlinear controller are designed respectively to realize dislocated control and dislocated synchronization of the system under the action of the controllers.The sufficient conditions for the realization of the control and synchronization of the system are obtained by theeiretical analysis.And the effectiveness of the methods are verified by numerical simulation using Matlab software.Secondly,one new complex chaotic system is proposed,baesd on the above three dimensional real system.The dynamic behavior of the system is analyzed,and the chaos control and generalized synchronization of the system are studied.The chaos control is realized by linear feedback control theory,and then,based on Lyapunov stability theory and the generalized synchronization principle the chaos generalized synchronization of this system is also gotten.Theoretical proof and numerical simulation verify the effectiveness of the method.Finally,the complete synchronization between real chaotic system and complex chaotic system is studied by feedback control theory.The synchronization between real Lorenz system and complex Lorenz system is studied as a example to verify the correctness of the method.