The Calculation Of The Maximum Lyapunov Exponent Of Chaotic Systems And Its Application In Eeg Data Analysis

The history and the current situation of the chaos science's development are introduced in the first chapter. Applies of the chaos in neural network and EEG analysis are also introduced in this chapter. In the second chapter, We introduce some of the Taken's reconstruction theories, the first of which is the foundation of our works. We proved it in detail.A new method of calculating the largest Lyapunov exponent from a urn-dimensional time series was proposed in the third chapter. The conception of average period was proposed for determining some important reconstruction parameters, which includes reconstruction dimensions. reconstruction delay and iteration numbers. The average period can also be useful to determine the reasonable sampling frequency and the minimum precise. We also improve the Wolf s algorithm, and overcome its handicap in calculating the largest Lyapunov exponent from the complex chaotic attractor. We can make full use of the time series by extending the permitted range of angle errors. The new method proved to be correct and efficient after testing many complex chaotic attractors.In the fourth chapter, we discuss the affection to the learning of BP neural network by setting initial values of the BP NN with the chaotic signals which have the variable threshold value range. At first, we prove by simulations that the random numbers generated by digital computer consist of chaotic series, and resetting the numbers randomly doesn't change its chaotic character. We use the different ranges of chaotic number as the initial connective weights. The results show: the same polarity of small chaotic numbers can improve learning efficiency of BP N7N about XOR problem, positive polarity of small chaotic numbers can improve learning efficiency of BP NN about symmetry problem.In the fifth chapter, we apply the method proposed in the third chapter to the EEG analysis. We must do some pretreatment due to the complex characteristic of EEG data. It includes: The high frequency components and the low frequency components of EEG data are filtered by FFT, The correlation dimension is calculated primarily to replace the original topological dimension. Then we can determine three reconstructed parameters in terms of average period. The results of EEG analysis show: The largest Lyapunov exponent of EEG data which corresponds to the hippocamp area is bigger than others. This manifests that the action of the hippocamp area is more active. The common feature is extracted from multi-channel EEG data by using the principal component analysis, and its potential significance is also predicted.