Fig. 4

Synaptic facilitation enhances the stability of discrete memory states. a Thefiring rate curve (solid, blue) and synaptic feedback (dashed red)for a system with feedback strength optimized for bistability in a group of cells withstatic synapses. Firing rate curve follows Eq. (34) with ${\beta }_1=119.5$, ${\beta }_2=0.615$, ${\beta }_3=5.326$, which is the best fit to the leaky-integrate and fireneuron used in the simulations and described in Table 2d.Feedback strength is optimized for bistability with $W=1.84$. b Same firing rate curve (solid, blue)as in a but synaptic feedback (dashed green) via facilitating synapseswith feedback strength optimized for bistability with $W=2.10$. a–b Solid circles indicate stablefixed points separated by an unstable fixed point (open circle). cDifference between firing rate and feedback curves in a and b determinethe basis for the gradient of an effective potential. Note the enhanced areas betweenfixed points (zero crossings) producing a larger potential barrier whensynapses are facilitating (green) compared to static (red). dThe lifetime of both the low activity state and the high activity state increasesexponentially with system size, but a given level of stability is achieved with farfewer cells when the synapses are facilitating (solid curves, analyticresults; filled and open circles simulated results for the high and lowactivity states, respectively)