Dynamic Behavior Analysis And Simulation And Control And Synchronization Of Two Class Of Chaotic Systems

In this paper,the problem of chaotic behaviors,chaos control and synchronization is investigated for two kinds of chaotic systems.Firstly,the related knowledge and research progress of chaos are introduced.Secondly,the whole process,which Willamowski-R?ssler chemistry system changes from periodic motions to chaotic motions through double-period bifurcation is simulated.We present bifurcation diagram,Lyapunov exponent spectrum,Poincare section,power spectrum and return map of the system,and the chaos behavior of the model are revealed.The adaptive controller and nonlinear controller were proposed,theoretical analysis and numerical simulation show that the chaos of the non-dimensional form of Willamowski-R?ssler system can be controlled effective.Drive-Response method is used to realize the global exponentially synchronization.The numerical simulation results show that the method is effective.Thirdly,the local stability of the fractional-order laser system is studied.The chaos control and the adaptive synchronization of a fractional-order laser system were realized,and the synchronization between integer order Lorenz system and fractional-order laser system is achieved by using the feedback control method.Based on stability theory,the correctness of the proposed methods is strictly demonstrated,the numerical simulation results further show their effectiveness.Finally,a four-dimensional hyper chaotic laser system is presented by adding a nonlinear controller to three-dimensional laser system,and the existence of the hyper chaos is validated.The globally attractive set and positively invariant set of the system are discussed by construct a family of generalized radically infinite and positive definite Lyapunov functions.The adaptive control for synchronization of the hyper chaotic laser system with time delay via a single variable is achieved.By using the feedback control method,the synchronization between integer order hyper chaotic Lorenz system and fractional-order hyper chaotic laser system is achieved.Based on stability theory,the correctness of the proposed methods are strictly demonstrated,the numerical simulation results further show their effectiveness.