Research On The Time Series Analysis Methods For Nonlinear System

In nature and society, most of phenomena are the nonlinear phenomenon.The linear rulesare only an approximation to the nonlinear rules. With the rapid development of nonlineardynamics in the second half of the20th century (especially, after chaos has been discovered), theresearch of nonlinear problems reached its climax, and many new theories and methods havebeen proposed successively. Among these methods, the time series analysis methods fornonlinear system have become an important research direction, which played more and moreimportant role in many fields.In this thesis, the classic chaotic systems(for example, the Lorenz system) and EEG areresearched and analyzed in a relatively all-sided way by using some modern analysis methods，such as PCA、wavelet analysis and nonlinear dynamics method. The main research work in thisthesis includes:1. Some Characteristic quantities which reflect the features of time series of nonlinearsystem and their computing methods are introduced in detail.Then, some chaotic systems such asLorenz, R ssler are described by these features.2. In view of the covariance matrix or coefficient matrix of the traditional principalcomponent analysis fail to reflect nonlinear correlation, the nonlinear principal componentanalysis is proposed by using the mutual information to replace the covariance or the corfficient.Then the correlation characteristics of the semgented EEG time series is researched by thismethod.3. We reconstructed the phase space of nonlinear time series by mutual informationmethod based on symbolic analysis and Cao algorithm, and the impact of symbolic parameterson the selection of optimal delay time is analyzed. In view of the subjective problem that existsin the Cao algorithm for determining the minimum embedding dimension, a criteria for thedetermination of minimum embedding dimension is given.Then both the approximate entropyand the permutation entropy of EEG are analyzed and investigated based on the phase spacereconstruction.4. In view of the non-stationary variation characteristics of nonlinear time series,thewavelet analysis method is employed to research nonlinear time series. Firstly，the waveletanalysis theory is introduced in detail.According to the wavelet theory, both the wavelet varianceand the wavelet subband entropy are proposed based on window function for the analysis of dynamic features of EEG under different physiological states.