Fig. 3: A simplified model for studying the relationships between brain system activity and connectivity.

a We constructed a dynamical model of a 4-, 192-, and 400-oscillator representation of either the four systems (default mode, DM;  frontoparietal subnetworks, SN-A & SN-B; and dorsal attention, DA) of interest (4- and 192-oscillator systems), or of the entire brain (400-oscillator system). Here, we show a representation of this oscillator network consisting of the frontoparietal subnetwork (A), the frontoparietal subnetwork (B), the default mode system, and the dorsal attention system. The remaining oscillators are not shown here representing all other regions of the brain used in the 400-oscillator model. b The network dynamics were integrated out to a total time of 6 min, consistent with the length of the empirical n-back scan. c Using four oscillators, increasing the amplitude of subnetwork (A) activity, while keeping all others equal, caused an increase in the functional connectivity between the frontoparietal and default mode units (Pearson correlation coefficient between unit timeseries: r = 0.396, p = 0.001), while increasing the amplitude of subnetwork (B) activity caused a decrease in the functional connectivity between the frontoparietal and default mode units (Pearson correlation coefficient between unit timeseries: r = −0.866, p < 0.0001). d Using 192 oscillators, increasing the amplitude of subnetwork (A) activity caused an increase in the functional connectivity between the frontoparietal and default mode units (r = 0.753, p = 0.001), while increasing the amplitude of subnetwork (B) activity caused a decrease in the functional connectivity between the frontoparietal and default mode units (r = −0.599, p < 0.0001). e Using 400 oscillators, increasing the amplitude of subnetwork (A) activity caused an increase in the functional connectivity between the frontoparietal and default mode units (r = 0.453, p = 0.011), while increasing the amplitude of subnetwork (B) activity caused a decrease in the functional connectivity between the frontoparietal and default mode units (r = −0.394, p = 0.031). Note that panel (e) contains the results of 30 simulations, in contrast to the 200 simulations depicted in panels c and d; this difference is due to the marked increase in computational burden in the 400-oscillator model.