Bifurcation diagrams depict the state space of the E-I system in terms of the mean external input currents to both subpopulations α ∈ {E, I}. (a) Bifurcation diagram of mean-field model without adaptation with up and down-states, a bistable region bi (green dashed contour) and an oscillatory region LC_EI (white solid contour). (b) Diagram of the corresponding AdEx network with N = 50 × 10³ neurons. (c) Mean-field model with somatic adaptation. The bistable region is replaced by a slow oscillatory region LC_aE. (d) Diagram of the corresponding AdEx network. The color in panels a—d indicate the maximum population rate of the excitatory population (clipped at 80 Hz). (e) Example time series of the population rates of excitatory (red) and inhibitory (blue) populations at point A2 (top row) which is located in the fast excitatory-inhibitory limit cycle LC_EI, and at point B3 (bottom row) which is located in the slow limit cycle LC_aE. (f) Time series at corresponding points for the AdEx network. All parameters are listed in Table 1. The mean input currents to the points of interest A1-A3 and B3-B4 are provided in Table 2.

https://doi.org/10.1371/journal.pcbi.1008717.g001