An Analysis on Lyapunov Spectrum of Electroencephalographic (EEG) Potentials

Tohru IKEGUCHI; Kazuyuki AIHARA; Susumu ITOH; Toshio UTSUNOMIYA

An Analysis on Lyapunov Spectrum of Electroencephalographic (EEG) Potentials

Tohru IKEGUCHI, Kazuyuki AIHARA, Susumu ITOH, Toshio UTSUNOMIYA

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Electroencephalographic (EEG) potentials are analysed by the Lyapunov spectrum in order to evaluate the orbital instability peculiar to deterministic chaos quantitatively. First, the Lyapunov spectra are estimated to confirm the existence of chaotic behavior in EEG data by the optimal approximation of Jacobian matrix in the reconstructed statespace. Second, the same method is applied to a neural network model with chaotic dynamics, the macroscopic average activity of which is analysed as a simple model of EEG data. The first analysis shows that the largest Lyapunov exponent is actually positive in the EEG data. On the other hand, the second analysis on the chaotic neural network shows that the positive largest Lyapunov exponent can be obtained by observing only the macroscopic average activity. Thus, these results indicate the possibility that one can know the existence of chaotic dynamics in the brain by analysing the Lyapunov spectrum of the macroscopic EEG data.

Publication: IEICE TRANSACTIONS on transactions Vol.E73-E No.6 pp.842-847

Publication Date: 1990/06/25

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Type of Manuscript: Special Section PAPER (Special Issue on Engineering Chaos)

Category: Chaos in Engineering Science

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Tohru IKEGUCHI
Kazuyuki AIHARA
Susumu ITOH
Toshio UTSUNOMIYA

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Tohru IKEGUCHI, Kazuyuki AIHARA, Susumu ITOH, Toshio UTSUNOMIYA, "An Analysis on Lyapunov Spectrum of Electroencephalographic (EEG) Potentials" in IEICE TRANSACTIONS on transactions, vol. E73-E, no. 6, pp. 842-847, June 1990, doi: .
Abstract: Electroencephalographic (EEG) potentials are analysed by the Lyapunov spectrum in order to evaluate the orbital instability peculiar to deterministic chaos quantitatively. First, the Lyapunov spectra are estimated to confirm the existence of chaotic behavior in EEG data by the optimal approximation of Jacobian matrix in the reconstructed statespace. Second, the same method is applied to a neural network model with chaotic dynamics, the macroscopic average activity of which is analysed as a simple model of EEG data. The first analysis shows that the largest Lyapunov exponent is actually positive in the EEG data. On the other hand, the second analysis on the chaotic neural network shows that the positive largest Lyapunov exponent can be obtained by observing only the macroscopic average activity. Thus, these results indicate the possibility that one can know the existence of chaotic dynamics in the brain by analysing the Lyapunov spectrum of the macroscopic EEG data.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e73-e_6_842/_p

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@ARTICLE{e73-e_6_842,
author={Tohru IKEGUCHI, Kazuyuki AIHARA, Susumu ITOH, Toshio UTSUNOMIYA, },
journal={IEICE TRANSACTIONS on transactions},
title={An Analysis on Lyapunov Spectrum of Electroencephalographic (EEG) Potentials},
year={1990},
volume={E73-E},
number={6},
pages={842-847},
abstract={Electroencephalographic (EEG) potentials are analysed by the Lyapunov spectrum in order to evaluate the orbital instability peculiar to deterministic chaos quantitatively. First, the Lyapunov spectra are estimated to confirm the existence of chaotic behavior in EEG data by the optimal approximation of Jacobian matrix in the reconstructed statespace. Second, the same method is applied to a neural network model with chaotic dynamics, the macroscopic average activity of which is analysed as a simple model of EEG data. The first analysis shows that the largest Lyapunov exponent is actually positive in the EEG data. On the other hand, the second analysis on the chaotic neural network shows that the positive largest Lyapunov exponent can be obtained by observing only the macroscopic average activity. Thus, these results indicate the possibility that one can know the existence of chaotic dynamics in the brain by analysing the Lyapunov spectrum of the macroscopic EEG data.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - An Analysis on Lyapunov Spectrum of Electroencephalographic (EEG) Potentials
T2 - IEICE TRANSACTIONS on transactions
SP - 842
EP - 847
AU - Tohru IKEGUCHI
AU - Kazuyuki AIHARA
AU - Susumu ITOH
AU - Toshio UTSUNOMIYA
PY - 1990
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E73-E
IS - 6
JA - IEICE TRANSACTIONS on transactions
Y1 - June 1990
AB - Electroencephalographic (EEG) potentials are analysed by the Lyapunov spectrum in order to evaluate the orbital instability peculiar to deterministic chaos quantitatively. First, the Lyapunov spectra are estimated to confirm the existence of chaotic behavior in EEG data by the optimal approximation of Jacobian matrix in the reconstructed statespace. Second, the same method is applied to a neural network model with chaotic dynamics, the macroscopic average activity of which is analysed as a simple model of EEG data. The first analysis shows that the largest Lyapunov exponent is actually positive in the EEG data. On the other hand, the second analysis on the chaotic neural network shows that the positive largest Lyapunov exponent can be obtained by observing only the macroscopic average activity. Thus, these results indicate the possibility that one can know the existence of chaotic dynamics in the brain by analysing the Lyapunov spectrum of the macroscopic EEG data.
ER -