Self-Correlations of Electroencephalograms

A susceptible-infected-susceptible (SIS) cellular automaton model for collective neural interactions proposed recently is revisited. In this model, neurons are simple network nodes with different states: active or firing, and quiescent. The main thesis of this approach is that the electroencephalogram (EEG) could emerge as the fluctuations in the number of firing neurons. In this framework, EEG is understood as a statistical epiphenomenon. In this paper, the mean number of active sites and the self-correlation function both in the SIS stochastic model and in elementary cellular automata (ECAs) are considered. Damped oscillatory relaxation to the stationary state is found both in the SIS model and in ECA rule 30; periodic oscillations are found for other class 3 and class 4 cellular automata. A statistical analysis of the selfcorrelations in real EEG shows that the damped oscillatory relaxations are found both in delta and alpha waves. The normalized amplitude of these correlations is predicted by cellular automata models. This reinforces the view of the brain as a highly complex cellular automata system.