Chaos Analysis And Feedback Control Of Memristor Load Nonlinear Circuit

The chaotic phenomenon of nonlinear circuits exists widely,and the analysis and control of the chaotic phenomenon are of great significance.In this thesis,the nonlinear dynamic characteristics of three-dimensional Lü system,Chua’s circuit and Cuk converter are analyzed,and the feedback control method and Hamilton energy control method are further studied.The main work and achievements of this thesis are as follows.(1)Study the dynamics of nonlinear systems.Taking the three-dimensional Lü system as an example to study,analyze the symmetry and dissipation of the Lü system,and find its bifurcation behavior;through its phase diagram,bifurcation diagram,Lyapunov exponent and Pioncare section,it is found that its existence period,quasi Period,transient chaos and other phenomena.(2)Research on feedback control methods for nonlinear systems.Explore the differential feedback control,external force feedback control,output feedback control and external excitation control of the Lü system.Furthermore,based on the Lü system,based on the mean field theory and Helmholtz theorem,the Hamiltonian energy of the system is calculated,the change of Hamiltonian energy with time under different motion states is studied,and the system is controlled.Simulation experiments show that the Hamilton energy can control the threedimensional Lü system in different states.(3)The Hamilton energy control method for smooth systems is studied.Taking memristorloaded Chua’s circuit as an example to study,establish its state equation model,analyze its basic dynamic behavior,study its chaotic attractor,coexisting attractor and its existence interval;based on Hopf bifurcation theory,analyze and study the circuit’s behavior.Hopf bifurcation point,determine the type of Hopf bifurcation point;study the relationship between Hamilton energy and circuit state variables,and propose a Hamilton energy control method for memristor-loaded Chua’s circuit.Simulation experiments show that Hamilton energy can control the circuit in different states.(4)The Hamilton energy control method for switching systems is studied.Taking the memristor-loaded Cuk converter as an example,the working principle and dynamic behavior of the memristor-loaded Cuk converter are studied;the Hamiltonian energy of the two subsystems of the Cuk converter is calculated,and the Hamiltonian energy of the two subsystems is unified by introducing a coupling coefficient;Use Hamilton energy to control the working state of the Cuk converter.Simulation experiments show that by choosing appropriate control coefficients and coupling coefficients,Hamilton energy can control the magnetron memristive load Cuk converter in a stable periodic state.