Figure 1.

Exemplary data (one representative subject in A,C) from different areas of the schematic Arnold tongue (synthetic data in B). If the stimulation properties (frequency/intensity) fall inside the Arnold tongue (triangular shaped color gradient in B), EEG and flicker show phase clustering (green phase plot in C) while outside the Arnold tongue Δ phase angles are randomly distributed (lilac phase plot in C). (A) Phase difference between stimulation and EEG signal over time. Each plot represents one stimulation frequency, from IAF (individual alpha frequency, Δ0 Hz) to Δ3 Hz in 1 Hz steps. All five stimulation intensities are shown. The asterisk and arrow in (A) mark an exemplary horizontal plateau of zero phase difference (synchronization, ^*), and an exemplary phase slip (↖), respectively. At Δ3 Hz phase drift was observed for the five intensities. (B) Schematic view of the hypothesized Arnold tongue (synthetic data). Within the Arnold tongue (green area) the intrinsic oscillator (EEG) is synchronized to the external stimulation. Outside the Arnold tongue (lilac area) EEG and external stimulation constantly show a phase drift. At the border (blue area), switches between the two states can be observed. Each square of the grid demonstrates one of the 35 stimulation condition. (C) Based on the data from (A) (third plot), three exemplary polar plots of the distribution of phase differences are shown for Δ 2Hz (12 Hz in this subject) and three stimulation intensities (1, 3, and 5). Top (intensity level 5): phase clustering was revealed by relatively high normalized Shannon entropy ($\tilde{\rho }$ = 0.0742). Bottom (intensity level 1): outside the Arnold tongue, Δ phase angles between EEG and stimulation signal are equally distributed in the phase plane. The normalized Shannon entropy $\tilde{\rho }$ as the quantitative measure is relatively low (0.0047).