A recent neurophysical model of propagation of electrical waves in the cort
ex is extended to include a physiologically motivated subcortical feedback
loop via the thalamus. The electroencephalographic spectrum when the system
is driven by white noise is then calculated analytically in terms of physi
ological parameters, including the effects of filtering of signals by the c
erebrospinal fluid, skull, and scalp. The spectral power at low frequencies
is found to vary as f(-1) when awake and f(-3) when asleep, with a breakpo
int to a steeper power-law tail at frequencies above about 20 Hz in both ca
ses; the f(-1) range concurs with recent magnetoencephalographic observatio
ns of such a regime. Parameter sensitivities are explored, enabling a model
with fewer free parameters to be proposed, and showing that spectra predic
ted for physiologically reasonable parameter values strongly resemble those
observed in the laboratory. Alpha and beta peaks seen near 10 Hz and twice
that frequency, respectively, in the relaxed wakeful state are generated v
ia subcortical feedback in this model, thereby leading to predictions of th
eir frequencies in terms of physiological parameters, and of correlations i
n their occurrence. Subcortical feedback is also predicted to be responsibl
e for production of anticorrelated peaks in deep sleep states that correspo
nd to the occurrence of theta rhythm at around half the alpha frequency and
sleep spindles at 3/2 times the alpha frequency. An additional positively
correlated waking peak near three times the alpha frequency is also predict
ed and tentatively observed, as are two new types of sleep spindle near 5/2
and 7/2 times the alpha frequency, and anticorrelated with alpha. These re
sults provide a theoretical basis for the conventional division of EEG spec
tra into frequency bands, but imply that the exact bounds of these bands de
pend on the individual. Three types of potential instability are found: one
at zero frequency, another in the theta band at around half the alpha freq
uency, and a third at the alpha frequency itself.