Proceedings of the National Academy of Sciences · 1986 · 763 citations · 5 references
Cognitive ScienceNeurodynamicsChaos TheoryNeurophysiologyComputational NeuroscienceEntropyBrain AttractorsHigh-dimensional ChaosLow-dimensional ChaosNeurologyNeuroscienceChaotic MixingAttractorElectroencephalographyLow DimensionalitySocial Sciences
The study explores the potential implications of low‑dimensional chaotic dynamics in epilepsy for biological and medical research. The authors compare epileptic attractors to those of normal brain activity and use autocorrelation and largest Lyapunov exponent analyses to characterize the underlying dynamics. EEG recordings of a human seizure reveal a deterministic chaotic attractor with a very low dimension (≈2.05) that sharply contrasts with the higher dimensionality (≈4.05) of normal deep‑sleep dynamics.
Using a time series obtained from the electroencephalogram recording of a human epileptic seizure, we show the existence of a chaotic attractor, the latter being the direct consequence of the deterministic nature of brain activity. This result is compared with other attractors seen in normal human brain dynamics. A sudden jump is observed between the dimensionalities of these brain attractors (4.05 +/- 0.05 for deep sleep) and the very low dimensionality of the epileptic state (2.05 +/- 0.09). The evaluation of the autocorrelation function and of the largest Lyapunov exponent allows us to sharpen further the main features of underlying dynamics. Possible implications in biological and medical research are briefly discussed.
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