A low-dimensional, compact brain model has recently been developed
based on physiologically based mean-field continuum formulation of
electric activity of the brain.
The essential feature of the new compact model is
a second order time-delayed differential equation
that has physiologically plausible terms, such as rapid corticocortical
feedback and delayed feedback via extracortical pathways.
Due to its compact form, the model facilitates insight into
complex brain dynamics via standard linear and nonlinear techniques.
The model successfully reproduces many features of previous models and
For example, experimentally observed typical rhythms of
electroencephalogram (EEG) signals are reproduced in
a physiologically plausible parameter region.
In the nonlinear regime, onsets of seizures, which often develop
into limit cycles, are illustrated by modulating model parameters.
It is also shown that a hysteresis can occur
when the system has multiple attractors.
As a further illustration of this approach, power spectra of the model
are fitted to those of sleep EEGs of two subjects
(one with apnea, the other with narcolepsy).
The model parameters obtained from the fittings show good matches
with previous literature.
Our results suggest that the compact model can provide a theoretical
basis for analyzing complex EEG signals.