Figure 1. Up and Down states and Up-and-Down transitions in two different network models.

(A) Model A (mean-field model) [18]: time-series for the membrane potential, . Observe the presence of two steady states lower one around mV (Down-state/blue curve) and a larger one (Up state/green curve) at about mV; these two are obtained for low noise amplitudes ( mV, ) and different initial conditions. Instead, the Up-and-Down state (red curve), corresponds to a high noise amplitude (, ). Note that, typically the Up-state intervals start with an abrupt spike which parallels empirical observations as discussed in [18]. Parameters have been fixed as in [18]: s, s, mV/Hz, , mV, mV, and Hz/mV. (B) Model B (network of spiking neurons) [21]: Time series of membrane potential. Curves and color code are as for Model A. For the system exhibits Up-and-Down transitions, for larger (smaller) values as (), it remains steadily in the Up (Down) state. Parameters have been fixed as in [21]: vesicles per synapsis , resting potential mV, membrane threshold mV, capacitance pF, leakage characteristic time s, synaptic recovery time s, signal time decay s, refractory period s, input amplitudes pA, pA, and external driving rate Hz.