Periodic and non-periodic brainwaves emerging via random syncronization of closed loops of firing neurons

Periodic and nonperiodic components of electrophysiological signals are modelled in terms of syncronized sequences of closed loops of firing neurons correlated in Markov chains. Single closed loops of firing neurons reproduce fundamental and harmonic components, appearing as lines in the power spectra at frequencies ranging about 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 the fluctuations of the number of syncronized loops leads to the onset of broadband power spectral components. By effect of the fluctuations of the number of synchronized loops and the emergence of the related broadband component, highly distorted waveform and nonstationarity of the signal are observed, consistently with empirical EEG and MEG signals. The analytical relationships of the periodic and aperiodic components are evaluated by using typical firing neuron pulse amplitudes and durations.