Nonlinear Chaotic Circuit And Its Dynamics Analysis

The phenomenon of chaos is the internal random process of the nonlinear system,which is extremely sensitive to the initial condition of the system. Lots of researchesindicate that the chaos phenomenon has wide application prospect and also has closeconnection with the engineering technology.Firstly, based on a third order autonomous system, we study the basic dynamiccharacteristics deeply. In this paper, we analysis the dimensions of the systems andthe maximum Lvapunov index and get the Matlab mumerical simulation diagram,Lvapunov exponential spectrum and bifurcation diagram, emphasizing on theinfluence of the basic dynamic characteristics caused by the different parameters.Moreover, the hardware circuit and Pspice software simulation software areproposed to verify the validity of the analysis.Secondly, we design a simple third order memristor circuit and analysis thenonlinear chaotic circuit based on the memristor. On the basis of the equation of thestate, bifurcation diagram, phase diagram and the time domain waveform figure isproposed to analysis the dynamic influence under the different parameters.Lastly, we design the sliding mode controller based on the exponential reachingrate and study the bifurcation and chaos phenomenon based on sliding mode control.We build the discrete iterative mapping model of the exponential reaching controlsystem and analysis the folding and bifurcation diagram of the different controllerparameters, according to the operating principle of sliding mode control ofsingle-phase inverter H bridge the under the single polarity modulation. We get thetime domain waveform figure of load current under the different parameters ofcontroller by the simulation software Matlab/Simulink to verify the correctness ofthe analysis. Bifurcation is provided to analysis the nonlinear characteristic when theinput voltage E and the inductor L change.