Schematic bifurcation diagram (not to scale, top panels) of the mean-field for the network with randomly-distributed <i>η</i>_<i>i</i> (bottom panels); some neurons are bistable (blue), and others tonic (red), with distribution centred at .

The ε = 0 equilibria lie on S-shaped curve (grey), whose folds occur for strictly negative values of K. The up state is now a high-voltage, high-rate equilibrium. The geometry of excitability persists when ε ≪ 1, and K(t) oscillates slowly around . (a): Down-down and down-up transitions for predominantly bistable distributions (). (b): Up-up and up-down transitions for predominantly tonic distributions ().