Dynamics Analysis And Control Of Unified Chaotic System With Hidden Attractor

Chaotic motion is an important research object in nonlinear dynamic system,and has become a hot topic in recent decades because of its wide application in the production and life of nature and human society.Especially in some frontier fields of science and technology,engineering technology also has considerable research value and application prospect.Among them,the chaotic system with hidden attractors is a new hot spot in nonlinear systems.In this thesis,theoretical derivation and MATLAB digital simulation are used to study the hidden attractor phenomenon in generalized Lorenz system and the synchronization problem of generalized Lorenz system.The synchronization problem of complex generalized Lorenz system is summarized as follows.The first part focuses on the coexistence of several different attractors in the generalized Lorenz system.With the condition of the chaotic characteristics of generalized Lorenz system,it analyzes the hidden attractors generated by generalized Lorenz system,and discusses the basic dynamical behavior of the system.Then it further discusses the parameter selection of hidden attractors for generating generalized Lorenz system as well as the influence of the selected values of different parameters c in the generalized Lorenz system on the motion change of the attractor,and finally the dynamic behavior is verified by MATLAB numerical simulation.The second part is the study of uniform generalized projective synchronization for generalized Lorenz system.As for the generalized Lorenz system,the controller and a synchronization error system are designed based on the Lyapunov stability theory,that is,different synchronization modes can be obtained when the appropriate variables are selected through the error system.The third part is the research of uniform projective synchronization for complex generalized Lorenz system.Based on the above generalized Lorenz system,it puts forward a new complex chaotic system,complex generalized Lorenz system.Firstly,it analyzes and studies the dynamical behavior of complex generalized Lorenz synchronously.Chaos synchronization of complex generalized Lorenz system is realized by using Lyapunov theory and unified generalized projective synchronization scheme.