Research On Electric Biological Signal Processing And Chaos Synchronization Of Neural Networks

Nonlinear science is a foundational discipline which concems the common properties of nonlinear phenomena.It is hailed as one of the three main revolutions in natural science in the 20^th century.Chaos theory is one important subdiscipline of nonlinear science.Wavelet analysis is the acknowledged time-frequency analysis method in the world.It has well local quality in the time-frequency fields and is named as "mathematics microscope".In this dissertation,based on chaos theory and wavelet theory,the electric biological signal processing and chaos synchronization of neural networks are explored and investigated. The main achievements contained in the research are as follows:Firstly,the nonlinear dynamics of the epilepsy electroencephalogram(EEG) of children are deeply studied.In most researches on EEG,the original EEG signals are analyzed.There is much interference in the original epilepsy EEG signals.It is easy to mix the interference with the spikes in the epilepsy signals.This will cause wrong analysis results.In this chapter, independent component analysis(ICA) is first adopted to isolate the epileptiform signals from the background EEG signals.Thus,errors caused by interference can be avoided.Then,the phase graph,power spectra,correlation dimension and Lyapunov exponents are studied comparatively.The results show that the phase graph,power spectra,correlation dimension and Lyapunov exponents of the EEG independent components reflect the general dynamical characteristics of brains,which can be taken as a quantitative index to weigh the healthy states of brains.Under normal physiological conditions,the EEG signals are chaotic;while under epilepsy conditions the signals approach regularity.Secondly,compression algorithms for two-dimensional(2-D) electrocardiogram(ECG) data are proposed.By studying the ECG waveforms,it can be concluded that the ECG signals generally show two types of correlation,namely the intrabeat correlation and the interbeat correlation.However,most existing ECG compression techniques do not utilize the interbeat correlation.In this chapter,a 1-D ECG data is first sliced and aligned to a 2-D data array,thus the two kinds of correlation of heartbeat signals can be fully utilized.And then 2-D wavelet transform is applied to the constructed 2-D ECG data array.Two compression methods are proposed according to the characteristics of the wavelet coefficients.Set partitioning hierarchical trees(SPIHT) algorithm and vector quantization(VQ) algorithm are modified. Records selected from the MIT/BIH arrhythmia database are tested contrastively using the proposed algorithm,some compression algorithms based on wavelet transform and the other 2-D ECG compression algorithms.The experimental results show that the proposed methods are suitable for various morphologies of ECG data,and that they can achieve higher compression ratios with the characteristic features well preserved.Thirdly,based on the modified observer algorithm and the nonlinear control method,the author presents the systematic design procedures for phase synchronization,projective synchronization and generalized synchronization of chaotic and hyperchaotic systems. Theoretical analyses and numerical simulations further demonstrate the feasibilities and effectiveness of the proposed synchronization schemes.Some valuable and important results are as follows:â‘ A systematic approach to realize phase synchronization is proposed based on the state observer method and the pole placement technique.The phase synchronization of chaotic systems can be obtained by suitably selecting the eigenvalues of error systems.The proposed method overcomes the shortcomings of the phase synchronization method based on active control.It is simple and the convergence rate can be flexibly adjusted by choosing the eigenvalues.â‘¡New methods for projective synchronization and generalized synchronization are proposed based on the modified state observer method.The proposed schemes are not only suitable to autonomous chaotic systems,but also effective to hyperchaotie systems.The proposed methods are simple and robust.They are able to realize synchronization in a general class of nonlinear systems without the limitation of partial-linearity.â‘¢Using the nonlinear control theory,a control law is designed to achieve the generalized synchronization of hyperchaotic systems.If the error gain matrix is suitably chosen,the generalized synchronization between drive system and response system will be obtained.The designed controller not only can realize the generalized synchronization of hyperchaos systems with the same dimensions,but also is suitable to the generalized synchronization problems of systems with different dimensions.Fourthly,the problems of adaptive synchronization,projective synchronization and generalized synchronization of neural networks(NNs) are investigated.Based on the Lyapunov stability theory,an adaptive controller and the parameters update law are designed for unknown NNs.With the proposed method,synchronization of the coupled neurons can be achieved,without needing to consider the coupled strength.Furthermore,based on the modified nonlinear state observer algorithm,projective synchronization and generalized synchronization schemes are designed.The proposed schemes can be implemented easily,and the convergence rates of the errors can be adjusted by choosing the eigenvalues of the error systems.Numerical simulations of FitzHugh-Nagumo(FHN) neuron system,Winner-Take-All competitive neuron system and cellular neural network etc are provided to demonstrate the effectiveness of the proposed synchronization schemes. Fifthly,anti-synchronization and projective synchronization schemes are designed for delayed Cohen-Grossberg NNs.Limited speed of information transmission between neurons makes delays unavoidable.Based on the Lyapunov stability theory,controllers are designed for delayed Cohen-Grossberg NNs.Theoretical analyses verify the feasibility of the proposed schems.The convergence rate of the controller is very fast.The synchronizations can be achieved by appropriately choosing the controller gain matrices.Numerical simulations demonstrate that the proposed synchronization schemes are general and robust.Sixthly,combining the adaptive technique,observer algorithm and fuzzy theory,fuzzy observers are designed and adaptive fuzzy synchronization schemes for chaotic and hyperchaotic systems are proposed.Fuzzy controller is simple to design.It is robust and applicable to nonlinear systems.Adaptive synchronization and projective synchronization can be achieved by using the proposed schemes.Based on the Lyapunov stability theory,the feasibilities of the proposed schemes are proved theoretically.Numercial simulations are provided to verify the effectiveness of the schemes.The author would like to appreciate the joint supports to this project by the National Natural Science Foundation of China(60573172) and the Superior University Science Technology Research Project of Liaoning Province(20040081).