The EEG α wave mode shows chaotic characters and the frequency spectrum is entrained to the external photo-stimulation peak. This effect was observed exceedingly in the photo-sensitive children as compared with the n...The EEG α wave mode shows chaotic characters and the frequency spectrum is entrained to the external photo-stimulation peak. This effect was observed exceedingly in the photo-sensitive children as compared with the normal adults. The α spectrum shows asymmetric components with lower frequency-side tail. This spectrum shape could be realized from the computation in terms of the McCulloch-Pitts model and presented in comparison with the observed result. From this analysis, it turns out that the frequency spectrum analysis is most essential for the investigation of the EEG characteristics in comparison with simple waveform inspections in the time-passage. When light flashing frequencies come close to the alpha peak, the both peaks are fused in a giant single peak. These phenomena cannot be understood by the simple mechanical resonant theory but as discussed from the viewpoint of the soft chaotic dynamics of the neural network. Here the both peak intensities Iα and Iex are investigated under different conditions of ωex ωα, and ωα ωex, and it is shown that the entrainment effect is remarkably different in both cases. This result can be understood from the relating neuronal numbers and discussed.展开更多
Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spe...Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spectrum distribution range.展开更多
An algorithm based on the data-adaptive filtering characteristics of singular spectrum analysis (SSA) is proposed to denoise chaotic data. Firstly, the empirical orthogonal functions (EOFs) and principal components (P...An algorithm based on the data-adaptive filtering characteristics of singular spectrum analysis (SSA) is proposed to denoise chaotic data. Firstly, the empirical orthogonal functions (EOFs) and principal components (PCs) of the signal were calculated, reconstruct the signal using the EOFs and PCs, and choose the optimal reconstructing order based on sigular spectrum to obtain the denoised signal. The noise of the signal can influence the calculating precision of maximal Liapunov exponents. The proposed denoising algorithm was applied to the maximal Liapunov exponents calculations of two chaotic system, Henon map and Logistic map. Some numerical results show that this denoising algorithm could improve the calculating precision of maximal Liapunov exponent.展开更多
This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different ...This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.展开更多
Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime,...Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime, a nonlinear method is proposed based on the higher order statistics, on the other aspect, which characterizes the higher order singular spectrum (HOSS) of chaotic signals. All computations are done with Lorenz attractor, Rossler attractor and EEG(electroencephalogram) time series and the comparisions among these results are made. The experimental results show that the Lipschitz exponents and the higher order singular spectra of these signals are significantly different from each other, which indicates these methods are effective for studing the singularity of chaotic signals.展开更多
文摘The EEG α wave mode shows chaotic characters and the frequency spectrum is entrained to the external photo-stimulation peak. This effect was observed exceedingly in the photo-sensitive children as compared with the normal adults. The α spectrum shows asymmetric components with lower frequency-side tail. This spectrum shape could be realized from the computation in terms of the McCulloch-Pitts model and presented in comparison with the observed result. From this analysis, it turns out that the frequency spectrum analysis is most essential for the investigation of the EEG characteristics in comparison with simple waveform inspections in the time-passage. When light flashing frequencies come close to the alpha peak, the both peaks are fused in a giant single peak. These phenomena cannot be understood by the simple mechanical resonant theory but as discussed from the viewpoint of the soft chaotic dynamics of the neural network. Here the both peak intensities Iα and Iex are investigated under different conditions of ωex ωα, and ωα ωex, and it is shown that the entrainment effect is remarkably different in both cases. This result can be understood from the relating neuronal numbers and discussed.
文摘Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spectrum distribution range.
文摘An algorithm based on the data-adaptive filtering characteristics of singular spectrum analysis (SSA) is proposed to denoise chaotic data. Firstly, the empirical orthogonal functions (EOFs) and principal components (PCs) of the signal were calculated, reconstruct the signal using the EOFs and PCs, and choose the optimal reconstructing order based on sigular spectrum to obtain the denoised signal. The noise of the signal can influence the calculating precision of maximal Liapunov exponents. The proposed denoising algorithm was applied to the maximal Liapunov exponents calculations of two chaotic system, Henon map and Logistic map. Some numerical results show that this denoising algorithm could improve the calculating precision of maximal Liapunov exponent.
文摘This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.
基金Science Foundation of Educational Commission of Fujian Province of China (Grant NO:JAO04238)
文摘Based on the variations of wavelet transform modulus maxima at multi-scales, the singularity of chaotic signals are studied, and the singularity of these signals are measured by the Lipschitz exponent.In the meantime, a nonlinear method is proposed based on the higher order statistics, on the other aspect, which characterizes the higher order singular spectrum (HOSS) of chaotic signals. All computations are done with Lorenz attractor, Rossler attractor and EEG(electroencephalogram) time series and the comparisions among these results are made. The experimental results show that the Lipschitz exponents and the higher order singular spectra of these signals are significantly different from each other, which indicates these methods are effective for studing the singularity of chaotic signals.
