Making use of the Poincare map and the phase space reconstruct,studying the orbit distribution under the chaos state of Lorenz equation,we found that hte chaotic orbit has the order,and has fine layer structure,and this illustrates the fact that the chaos is the union of inherent randomness and the regularity froma new point of view.

The operating principle of three-phase PFC(Power Factor Correction)rectifier under OCC(One-Cycle Control)is analyzed and the mathematic switching model and equivalent control equation for three-phase OCC-PFC are derived,based on which,its working stability conditions and dynamic performance are derived based on Poincare mapping.

With the help of Poincare mapping,the stability problem of periodic orbits was changed to that of the fixed points on the mapping plane.

For improving the accuracy of the parameters,when utilizing laser Doppler effect to measure the parameters of the object,a novel approach of analyzing nonstationary signal was proposed,the system equation was deduced through the gradient search method,the stability of the system by the Poincaré map theory was studied.