Figure 4: Local and global structural properties jointly determine the complexity of whole-brain dynamics.

(a-c) show the bifurcation diagrams of the local model for three different types of local excitatory connectivity: (a) w_EE = 0.7 and w_EI = 0.35; (b) w_EE = 2 and w_EI = 1; (c) w_EE = 2.8 and w_EI = 1 (representatives of distinct dynamic regimes of the local model, Figure S1). Overall, local connectivity increases from (a) to (c). The activity of the excitatory population S_E is used as an order parameter, indicating the location of each attractor. The external input I_E is used as a control parameter. Each point in the diagram indicates the location of a particular fixed point. The color denotes the type of each fixed point: non-black points represent attractors, black points unstable fixed points that are not associated with a limit cycle. Horizontal stripes indicate that the attractors are changing continuously with the control parameter for a certain range. All (a)-(c) have an upper stripe and a lower stripe. (b)-(c) have an additional stripe in the middle, where the brain region oscillates. Insets of (b) and (c) show the oscillation frequency of the brain region as a function of the input current. Each stripe corresponds to a discrete level of activation for a single brain region (circled brains in b; color indicates discrete S_E levels, shown in circled legend). (d)-(f) show the corresponding bifurcation diagrams for three uniform global networks, i.e. the large-scale structural connectivity C_ij’s are identical between any two brain regions (equation 6). The average activity of all excitatory populations (${\overline{S}}_E$) is used as an order parameter and the global coupling G (equation 6) as a control parameter. Each attractor stripe corresponds to a pattern of activation over the whole brain (circled brains in (e) show $S_E^{(i)}\text{'}\text{s}$ on the left hemisphere). Similarly, (g)-(i) show the corresponding bifurcation diagrams for three realistic global networks, i.e. C_ij’s reflect the human connectome (see text for details). Here each vertical slice (gray line in h) contains the attractor repertoire of a fixed dynamic landscape shaped by the human connectome. Each attractor repertoire is associated with a matrix describing the coordination between brain regions across attractors (e.g. Figure 5b). See Figure 3 for a cartoon illustration of attractor repertoires and the associated cross-attractor coordination matrices.