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ZerlautAdaptationSecondOrder

Description

Second-order mean-field model of a conductance-based network of adaptive exponential integrate-and-fire (AdEx) excitatory and inhibitory neurons (di Volo et al. 2018, Zerlaut et al. 2018). It tracks the mean firing rates of the excitatory (E) and inhibitory (I) populations, their second-order statistics (the covariance matrix C_ee, C_ei, C_ii), the adaptation currents (W_e, W_i) and an Ornstein-Uhlenbeck noise drift (ou_drift). The population firing rate is given by a semi-analytic transfer function (TF) whose argument is the membrane-potential fluctuation regime (mu_V, sigma_V, T_V) and a phenomenological voltage threshold fitted by a second-order polynomial. The first and second derivatives of the transfer function with respect to the pre-synaptic rates are evaluated with the SAME central finite-difference stencil (df = 1e-7) used in the original TVB implementation, so the drift is reproduced bit-for-bit.

Parameters
NameValueUnit
g_L 10.0 tvbo.unit_enum(20,)
E_L_e -65.0 tvbo.unit_enum(9,)
E_L_i -65.0 tvbo.unit_enum(9,)
C_m 200.0 tvbo.unit_enum(17,)
b_e 60.0 tvbo.unit_enum(15,)
a_e 4.0 tvbo.unit_enum(20,)
b_i tvbo.unit_enum(15,)
a_i tvbo.unit_enum(20,)
tau_w_e 500.0 tvbo.unit_enum(2,)
tau_w_i 1.0 tvbo.unit_enum(2,)
E_e tvbo.unit_enum(9,)
E_i -80.0 tvbo.unit_enum(9,)
Q_e 1.5 tvbo.unit_enum(20,)
Q_i 5.0 tvbo.unit_enum(20,)
tau_e 5.0 tvbo.unit_enum(2,)
tau_i 5.0 tvbo.unit_enum(2,)
N_tot 10000
p_connect_e 0.05
p_connect_i 0.05
g 0.2
K_ext_e 400
K_ext_i
T 20.0 tvbo.unit_enum(2,)
P_e0 -0.04983106
P_e1 0.005063550882777035
P_e2 -0.023470121807314552
P_e3 0.0022951513725067503
P_e4 -0.0004105302652029825
P_e5 0.010547051343547399
P_e6 -0.03659252821136933
P_e7 0.007437487505797858
P_e8 0.001265064721846073
P_e9 -0.04072161294490446
P_i0 -0.05149122024209484
P_i1 0.004003689190271077
P_i2 -0.008352013668528155
P_i3 0.0002414237992765705
P_i4 -0.0005070645080016026
P_i5 0.0014345394104282397
P_i6 -0.014686689498949967
P_i7 0.004502706285435741
P_i8 0.0028472190352532454
P_i9 -0.015357804594594548
external_input_ex_ex
external_input_ex_in
external_input_in_ex
external_input_in_in
tau_OU 5.0 tvbo.unit_enum(2,)
weight_noise 10.5
S_i 1.0
State variables
NameInitial value
E 0.0
I 0.0
C_ee 0.0
C_ei 0.0
C_ii 0.0
W_e 0.0
W_i 0.0
ou_drift 0.0