Dynamic Behavior Analysis And Control And Synchronization Simulation Of Several Chaotic Systems

In this thesis,the problem of chaotic behaviors,chaos control and synchronization is investigated for several chaotic systems.Firstly,the related knowledge and research progress of chaos are introduced.Secondly,the dynamic behavior of the two Couette-Taylor flow systems are analyzed,and the numerical simulation is carried out.The evolution process of the corresponding Couette-Taylor flow is explained.The globally attractive set and positively invariant set of the two Couette-Taylor flow systems are discussed by constructing a family of generalized radically infinite and positive definite Lyapunov functions.The sufficient conditions of the estimation of the globally exponentially attractive set and positively invariant set are given by strict mathematical proof.Some feedback control laws are designed to guarantee that all the trajectories of the Couette-Taylor flow system track a periodically solution,or globally stabilize an unstable equilibrium.The designed linear feedback controller are effective in globally synchronizing two identical chaotic systems.A numerical example is provided to validate the feasibility of the result.Finally,the dynamic behavior and simulation of the earth's magnetic field system are discussed.We obtained the Lyapunov exponents diagram,bifurcation diagram,attractors diagram and Poincare section diagram of earth's magnetic field system,and drawn the phase space trajectories of earth's magnet system,thus the dynamic behavior of the earth's magnetic field system is described in detail.The globally exponentially attractive set and the positively invariant set of earth's magnetic system are achieved by construct a family of generalized radically infinite and positive definite Lyapunov functions.The linear feedback control law is designed to realize the globally exponential synchronization,and the effectiveness is verified by computer simulation.