Study On Control And Synchronization For Chaotic Systems And The Dynamic Behavior

Chaos is a special form of exercises in the nonlinear dynamical system, which hasbeen intensively studied and widespread in nature. In recent decades, with the rapiddevelopment of research in the field of chaos control, the control and synchronization ofChaos have been penetrated into many areas. In engineering technology, it has a veryimportant research value and application prospects. And it is concerned by dynamics andengineering control experts, making it become an active research of the nonlinear subject.In this paper, the development of chaos, the basic characteristics of chaoticdynamical behavior for control and synchronization of chaos and the related theories areintroduced. The theoretical analysis and numerical simulation methods are utilized in thisthesis. For the control and synchronization of two nonlinear chaos systems, we do somepositive studies. The main content is depicted as follows:Firstly, for the Mathieu-Duffing chaotic system with forced and damping, the systembehavior is firstly analyzed by the Lyapunov exponents of chaotic dynamics. Then, basedon Lyapunov stability theory and passivity adaptive control appropriate adaptivecontroller is designed to make the system stable at any one expected unstable point, therobustness of uncertain parameters of the system is also studied. Numerical simulationswith Matlab are presented to show the effectiveness of our design. The feasibility of theadaptive controller is obtained further illustrates.Secondly, a new three-dimensional autonomous chaotic system control andsynchronization problems are firstly studied. On the basis of detailed analysis of itschaotic behavior, linear and nonlinear feedback control methods are used to designcontroller, a sufficient condition for controlling to unstable points are obtained. Againlinear feedback control method, nonlinear feedback control method and pulse controlmethod are utilized for the chaotic synchronization control, the sufficient conditions ofsynchronization also are given, the effectiveness of the methods is given to demonstrateby theories and numerical simulation.Finally, the generalized synchronization ideas are proposed, they are also used for thechaos synchronization; the strategy of rationale is verified.