A theory for self-sustained balanced states in absence of strong external currents
Fig 2
Finite-size characterization of the homogeneous stationary solutions.
(A) Stationary firing rates and synaptic efficacy as a function of the system size N. Symbols correspond to numerical simulations while the solid line shows the self-consistent mean field prediction (5). The solutions obtained in the thermodynamic limit (,
and
) are reported as dashed lines. Here we set J0 = 0.1 and I0 = 0. (B) Heatmap showing the combined effect of
on the firing rate of the excitatory neurons in a finite network with
obtained by using the mean-field predictions (5). The dashed lines indicate the cuts explored in (C) and (D). (C) Predicted excitatory firing rates at fixed J0 = 0.1 by varying I0 for different network sizes, in the inset are reported the corresponding stationary excitatory input currents
. As
the effect of the external current becomes negligible. (D) Same as in (C) by fixing I0 = 0.3 and varying J0, these results show the independence of the asymptotic solution from J0.