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Dynamics of brain electrical activity

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Summary

In addition to providing important theoretical insights into chaotic deterministic systems, dynamical systems theory has provided techniques for analyzing experimental data. These methods have been applied to a variety of physical and chemical systems. More recently, biological applications have become important. In this paper, we report applications of one of these techniques, estimation of a signal's correlation dimension, to the characterization of human electroencephalographic (EEG) signals and event-related brain potentials (ERPs). These calculations demonstrate that the magnitude of the technical difficulties encountered when attempting to estimate dimensions from noisy biological signals are substantial. However, these results also suggest that this procedure can provide a partial characterization of changes in cerebral electrical activity associated with changes in cognitive behavior that complements classical analytic procedures.

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Dedicated to the Memory of Hassler Whitney, 1907–1989.

Acknowledgment: PER would like to acknowledge NIH Grant NS19716, a grant from the Whitaker Foundation and the hospitality of the Department of Mathematics and Kingswood College at the University of Western Australia. TRB would like to acknowledge NIH Grants AG04581 and MH40627 and a grant from the Allegheny-Singer Research Foundation. JMM wishes to thank INRIA, Paris. AMA would like to acknowledge support from the Bryn Mawr College Faculty Committee on Awards and Grants. The continuing support of the College Computer Center of the Medical College of Pennsylvania is gratefully acknowledged. During the course of this research we have benefited from advice and instruction from many colleagues including E. Donchin, G. Goldberg, and R. N. Harner. The technical assistance of Joseph Waldron is gratefully acknowledged. We wish to express our thanks to UniSys Corporation for the generous donation of computer equipment to this project.

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Rapp, P.E., Bashore, T.R., Martinerie, J.M. et al. Dynamics of brain electrical activity. Brain Topogr 2, 99–118 (1989). https://doi.org/10.1007/BF01128848

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