Oscillatory processes of bioelectrical activity in the cerebral cortex

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 the average afferent input under the assumption that the cell threshold distribution is the normal distribution. 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 down to domination of the 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 was obtained. The occurrence of the non-regular spindle-shaped activity expanding frequency of the basic oscillation and widening spectral peak was revealed. 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 in the unsteady region.