B.V. Bakharev, M.N. Zhadin

The interaction between excitatory and inhibitory populations of neocortical neurons, taking into account the well-known nervous cells properties (the absolute and relative refractory periods, the postsynaptic potential amplitude dependence of the membrane potential) is considered. Steady states and the stability region of oscillations of average membrane potential of excitatory neurons, as is well known be accountable for electroencephalogram, are studied upon varying average afferent input under the assumption that the cell threshold distribution is normal. It is shown that there is a parameter range in the stability region where an increase of the average discrete Gaussian white-noise of nonspecific afferent input enhances the oscillation frequency up to the domination of determined rhythm followed by its attenuation and spectral spreading upon further increase of the input. The human and animal-s electroencephalograms in different functional states were numerically simulated. The real form of a power spectrum of electroencephalogram is obtained. In the unsteady region, the existence of a limiting cycle and possibility of arising of pathological activity observed at abnormal brain functioning were shown with the help of the numerical nonlinear analysis.