Fig. B1.
Bifurcation diagrams in 1-dimensional parameter spaces. In all panels, we show the value of the excitatory activity uE associated with equilibria and periodic orbits (in that case, maximal and minimal values are plotted) as a function of 1 given parameter. L1 and L2 show the influence of excitatory input IE for fixed α = 1 and κ = 3 (L1) or κ = 0.5 (L2). L3 and L4 elucidate the influence of κ with α = 1 and IE = 0.75 (L3) or IE = 1.5 (L4). L5 and L6 characterize the influence of α, with IE = 1.5 and κ = 4 (L5) or κ = 1.5 (L6). Regions are colored according to the type of stable solutions. We distinguish between up- and down-states when >1 solution is present for a given choice of the parameters, whereas we call it a generically stable active state when only 1 (stable) constant solution is present. Bifurcation labels: LP, limit point; H, Hopf; SH, saddle homoclinic; SNH, saddle node homoclinic; LPC, limit point of cycles. Solid (dashed) black lines represent stable (unstable) solutions for uE. Maximal and minimal uE along cycles are depicted in cyan (solid, stable; dashed, unstable limit cycles).