Dynamics Analysis And Synchronization Of Chaotic Systems

Chaotic systems are special nonlinear systems,which are deterministic dynamical systems exhibiting irregular,seemingly random behavior and depend sensitively on the initial conditions.They have significant applications in a large number of areas,such as image processing,information security,fault diagnosis,economy,and finance and etc.Therefore in recent decades,the design,control and synchronization of chaotic systems have attracted a great deal of attentions.In this thesis,several problems about dynamics analysis and synchronization of chaotic system are studied as follows:First,by introducing a nonlinear exponential function term,a new four-dimensional chaotic system with exponential function term is investigated.The dynamic properties of the new chaotic system are studied such as the equilibria and their stability,the dissipation and Lyapunov exponents,and the impact of different parameters on its dynamics.In addition,a twoinput adaptive controller is designed to achieve the synchronization of the new chaotic system.Second,the adaptive synchronization with less measurement and actuation for the chaotic system satisfying a less restrictive Lipschitz condition is studied.In other word,when the rank of the output matrix is less than or equal to the dimension of state space,could the adaptive synchronization be achieved by activating fewer controllers? A sufficient condition is given for the first time based on the Lyapunov stability theory.This result generalizes the relevant results in the existing literatures.Numerical simulations are presented to verify the correctness and effectiveness of theoretical results.Finally,a class of generalized hyperchaotic Lorenz-like systems is proposed,which can describe many well-known four-dimensional hyperchaotic systems including hyperchaotic Lorenz system,hyperchaotic Liu system and hyperchaotic Lü system,etc.Two-input nonlinear controllers are designed to achieve the control and synchronization based on partial feedback linearization.Moreover,for a special class of generalized hyperchaotic Lorenz-like systems,single-input controllers for the control and synchronization are also designed,respectively.