Periodic and Non-Periodic Brainwaves Emerging via Stochastic Syncronization of Closed Loops of Firing Neurons

Abstract

Periodic and non-periodic components of electrophysiological signals are modelled in terms of syncronized sequences of closed loops of firing neurons correlated according to a Markov chain. Single closed loops of firing neurons reproduce fundamental and harmonic components, appearing as lines in the power spectra at frequencies ranging from 0.5 Hz to 100 Hz. Further interesting features of the brainwave signals emerge by considering multiple syncronized sequences of closed loops. In particular, we show that fluctuations in the number of syncronized loops lead to the onset of a broadband power spectral component. By the effects of these fluctuations and the emergence of a broadband component, a highly distorted waveform and nonstationarity of the signal are observed, consistent with empirical EEG and MEG signals. The amplitudes of the periodic and aperiodic components are evaluated by using typical firing neuron pulse amplitudes and durations.