Dynamical Analysis And Synchronization Of A Class Of Chaotic Systems

Chaos is a seemingly random,irregular movement that is commonly found in deter-ministic system.Chaos has a wide range of applications,including in the fields of secure communication,biomedical engineering,electronic science and applied mathematics.This thesis considers a class of three-dimensional autonomous systems that contain a square term which are constructed in existing literature,but without detailed dynamical analysis.The thesis has studied dynamic characteristics,chaotic control and synchroniza-tion problems of the systems.The main conclusion of this thesis is as follows:Firstly,using the knowledge of chaos,The symmetry and invariance,dissipativeness and existence of the attractor,stability of the equilibrium points of the chaotic systems are analyzed theoretically.The systems' bifurcation and Poincare cross section,Lyapunov index,Lyapunov dimension,sensitivity to initial value and power spectrum are performed to verify the rich chaotic characteristics of the type of systems.Secondly,the thesis has studied the bounds of the chaotic system,that is,when the system parameters satisfiy certain conditions,the two limit estimation formulas of the relevant variables are obtained when the time approaches infinity.The feasibility of the limit inequality is numerically verified.Finally,in terms of chaotic control,the feedback control method is used to lin-earize the controlled system at the equilibrium points.According to the Routh-Hurwitz criterion,the control parameters are obtained to make the controlled system asymptoti-cally stable to the equilibrium points.For the research of chaotic synchronization,on the one hand,based on the local linearization stability analysis,a nonlinear feedback synchro-nization is used to construct a suitable controller to asymptotically stabilize the system to zero and achieve system synchronization.On the other hand,the adaptive controllers are designed to analyze self-adaptive synchronization and projective synchronization for chaotic systems with unknown parameters.Combining the Lyapunov stability theory and the LaSalle invariant principle,the proposed controller and the adaptive law of parame-ters axe proved theoretically.The effectiveness of the controllers are verified by numerical simulation and the unknown parameters can be accurately identified.