Figure 3
Examples of a three-channel model of bifrequencies interaction (Fig. 1) from channels \((X_1, X_2)\) to channel \(X_3\) in the 0–50 Hz range with cross-channel coupling strength varying from weak to strong (from left to right). Panels in rows (A) and (C) show the cross-bicoherence significance maps with only those bifrequencies (black bins) characterized by cross-bicoherence values different from zero (\(\overline{{b}^2_{ijk}}\), \(q < .05\)). Panels in rows (B) and (D) show the median unconditional bivariate Granger causality spectrum in a semi-logarithmic scale with a grey area corresponding to the integration over the curve of all significant values (with a threshold of significance represented by the dashed line) and a black area corresponding to the integration for the spectral interval of interest. (A, B) Analyses falling in sector \(Q_{\textrm{I}}\) at bifrequencies \(F_1 = ({120/2\pi })\) , \(F_2 = ({70/2\pi })\) indicated by the red labels and \(F_3 = ({80/2\pi })\) indicated by the blue label and arrow (i.e., \(F_1 \approx 19.1\) Hz, \(F_2 \approx 11.1\) Hz, \(F_3 \approx 12.7\) Hz). (C, D) Analyses falling in sector \(Q_{\textrm{II}}\) at bifrequencies \(F_1= ({50-10/2\pi })\), \(F_2 = ({230/2\pi })\) indicated by the red labels and \(F_3 = ({150/2\pi })\) indicated by the blue label and arrow (i.e., \(F_1 \approx 48.4\) Hz, \(F_2 \approx 36.6\) Hz, \(F_3 \approx 23.9\) Hz). In the plots, \(f_1\) and \(f_2\) correspond to the bifrequency coordinates of frequency parameters \((F_1, F_2)\).
