Chaos in the Brain: A Nonlinear Time Series Analysis of Electroencephalograms

Zakir Zulfikar Thaver

Following the experimental verification that a single neuron can generate chaos in neural activity, chaotic behavior in the macroscopic activity of the brain, which is essentially a set of neurons connected in a network, was anticipated. The electroencephalogram (EEG) is a crude measure of the electrical activity of the billions of neurons in the brain, and is considered to represent its macroscopic state. EEG Data from a young subject with eyes open and closed was analyzed using Chaos Data Analyzer, Professional version (CDA). The correlation dimension and Lyapunov exponents were calculated for all the EEG data using optimal embedding dimensions and time delays. The results for the EEG data from the young subject with eyes open from electrode 1 (Channel 1) placed according to the International 10-20 System, were compared with the corresponding results for Random and Chaotic data (from the Duffing equation). The correlational length (time) τ for the EEG data was more than that for the Random data but less than that for Duffing data, showing more correlation between temporal neighbor than the former but less than the latter. The correlation dimension Dc for EEG data was less than Random data but more Duffing data suggesting that EEG is not merely noise. More trend in separation was observed in the case of EEG data than Random data, but less than Duffing data. Specifically, while the largest Lyapunov exponent λ for Random data was found to tend to zero, that for Duffing and EEG were found to be positive indicating their chaotic nature. Moreover, for all the EEG data sets analyzed, the largest Lyapunov exponents λ were found to be positive. The results, within experimental error, suggest that the EEGs have significant chaotic character. The human brain can therefore be considered to be a giant nonlinear dynamic system, and hence can be modeled by nonlinear dynamic invariants.