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How single neuron properties shape chaotic dynamics and signal transmission in random neural networks
Fig 2
Self-consistent statistics in the chaotic regime.
a: Resonant (narrow-band) chaos. Power spectral density obtained from mean-field theory (solid line) and microscopic simulations (light blue, dashed) for γ = 0.25, β = 1 and g = 2gc(γ, β). The dashed, dark blue line indicates the square modulus of the linear response function 
for the same adaptation parameters. Inset: Normalized mean-field autocorrelation Cx(τ) for the same parameters, plotted against the time lag in units of τx. b: Non-resonant (broad-band) chaotic regime. Curves and inset are the same as in a, but with γ = 1, β = 0.1 and g = 2gc(γ, β). c: Maximum-power frequency fp of the recurrent network plotted against γ, for different β. Crosses depict results obtained from microscopic simulations, circles show the semi-analytical prediction based on the iterative method and dashed lines shows the theory based on the single neuron response function. For γ = 0 all curves start at fp = 0. d: Power spectral density Sx(f) for different levels of heterogeneity of the parameter β (solid lines), compared to the case without heterogeneity (dashed line). All the curves are almost superimposed, except at very low frequencies where small deviations are visible (inset). Parameters: γ = 0.25, 
, 
. e: Distributions P(x) of the activation x from microscopic simulation (N = 2000, solid lines) and theoretical prediction (dashed lines). The adaptation parameter were γ = 0.25 and β = 1. f: Normalized power spectral density 
(solid lines) at different iterations n, for the network with adaptation. For the first iterations, the powers of 
(dashed lines), provide a good approximations of the power spectrum width. The initial power spectral density is a constant and the network parameters are the same as in panel a.
doi: https://doi.org/10.1371/journal.pcbi.1007122.g002