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Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks
Fig 6
Mean-field theory prediction of the response dynamics: (A) Excitatory firing rates vs. input strength at the AS state, with 
. The red/blue markers represent network simulation results under noisy/constant inputs. The black curve represents the field model fixed-point estimation under fixed σα parameters indicated at the end of this caption. The purple curve represents the result under σα parameters estimated with different rin values. (B) The real part of the eigenvalue evaluated at equilibrium. The purple curve indicates the zero value (i.e., the deterministic Hopf bifurcation points), and the black curve corresponds to the case where the real part of the eigenvalue is −0.05. (C) The prediction of the population oscillation frequency f = ω/2π, where ω is the imaginary part of the eigenvalue at equilibrium. Only results above the effective critical black line in (B) are shown. The inset shows the frequencies for input strengths rin = 0.4, 0.65, 0.9/ms (solid and dotted lines correspond to the critical and supercritical cases with 
), similar to the inset of Fig 3E. (D) The linear noise prediction of Var(VE) for different 
and rin values (before the Hopf bifurcation line). The black curve is the critical line in (B). (E) Plot of Var(VE) vs. input strength rin for subcritical and critical states with 
. (F) Same as (E) but for quantity 
. The field equation parameters are σe = 3.2, σi = 3.8, β = 0.2.
doi: https://doi.org/10.1371/journal.pcbi.1009848.g006