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We present a model for the dynamics of a cerebral cortex in which inputs to neuronal assemblies are treated as random Gaussian fluctuations about a mean value. We incorporate the effect of general anesthetic agents on the cortex as a modulation of the inhibitory neurotransmitter rate constant. Stochastic differential equations are derived for the state variable h e, the average excitatory soma potential, coherent fluctuations of which are believed to be the source of scalp-measured electroencephalogram (EEG) signals. Using this stochastic approach we derive a stationary (long-time limit) fluctuation spectrum for h e. The model predicts that there will be three distinct stationary (equilibrium) regimes for cortical activity. In region I (“coma”), corresponding to a strong inhibitory anesthetic effect, h e is single valued, large, and negative, so that neuronal firing rates are suppressed. In region II for a zero or small anesthetic …