O.Yu. Panischev, S.A. Demin, M.R. Idiyatova
Paper demonstrates the new capabilities of memory function formalism as a useful analytical tool for studying the collective phenomena within a framework of the phase synchronization approach. The proposed method allows to study the collective effects in complex systems of the different nature with a few separate areas each of which have own dynamics. Capabilities of the presented theory are demonstrated by means of analyzing cross correlations between the neuromagnetic responses simultaneously obtained from multiple brain regions of healthy people and of a patient with photosensitive epilepsy. These responses were induced by chromatic flickering stimuli.
To identify the phase synchronization we use the power spectra of memory functions which are derived within the framework of memory function formalism, because we have revealed that if the power spectra of auto-correlation functions have peaks in equal frequencies then power spectrum of cross correlation function has the same peaks with higher amplitude. Thus they reflect the frequencies of processes which are general for both the considered signals and allow, on one hand to identify the phase synchronization, on the other hand, to determine the frequency band in which it take place.
The findings show that the brain signals of healthy people (control group) have the well-defined effects of phase synchronization and at the same time the domination of low-frequency processes. On the contrary, the neuromagnetic responses of a patient are characterized by a sharp abnormality of frequency synchronization, and also by prevalence of high-frequency quasi-periodic processes. Modification of synchronization effects can be a diagnostic criterion for detecting pathological abnormalities in brain activity at photosensitive epilepsy.