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
| Name | Value | Unit |
|---|---|---|
| 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
| Name | Initial 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 |