Research On Computational Method Of Chaotic Time Series And Its Application

Chaos theory is one of the three most important scientific revolutions in 20^th century .The idea that studying chaos based on time series has been developing rapidly since the phase space reconstruction theory came up in 1980s. This paper begins with the theory of chaotic time series, puts more emphasis on methods which can be used to decide if the time series is chaotic or not and summaries effective analyzing means to lay a solid foundation for further researches.This paper first briefly introduces the development of chaos theory, the research background and meaning and some typical chaotic time series like Logistic mapping, Lorenz equation, Chens strange attractor and Rossler strange attractor.Next it introduces the definition of chaos and the methods used to judge chaos like Poincare Section method, power spectrum method and characteristic quantity method. Then it discusses three important characteristic quantities Correlation Dimension, Kolmogorov Entropy and Lyapunov Exponent including definitions and algorithms of them and programming to realize the algorithms. And then it discusses some details of the algorithms including the selection of the optimal time delay and embedding dimension. Then introducing three main selection methods autocorrelation function method, mutual information method, C-C method and comparing them. At last, it applies chaotic time series theory to analyze the dynamic characteristic of large-size CNC milling machine and gains significative results.