This paper generalizes an existing continuum model of the large-scale elect
rical activity of the brain by incorporating local feedback. The model is f
irst reformulated by parametrizing neuronal function in more detail and we
then show that only four broad classes of local feedback are consistent wit
h general physiological constraints. The corresponding linear dispersion re
lations ale found to contain additional modes as a result of feedback. It i
s shown that each feedback class can produce lightly damped or undamped osc
illatory modes at frequencies similar to those seen in electroencephalograp
hy, although not all combinations of type and speed of feedback result in o
scillatory behavior. Three kinds of lightly damped resonances are found, ea
ch with distinctive frequency characteristics. The effect of feedback on ot
her roots is also described. [S1063-651X(99)05901-2].