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    Metadata details:
    filename: spm_fx_erp.m
    path of file: ./repos/spm/toolbox/dcm_meeg
    
    the code of the file until where you have to start completion: function [f,J,Q] = spm_fx_erp(x,u,P,M)
% State equations for a neural mass model of erps
% FORMAT [f,J,D] = spm_fx_erp(x,u,P,M)
% FORMAT [f,J]   = spm_fx_erp(x,u,P,M)
% FORMAT [f]     = spm_fx_erp(x,u,P,M)
% x      - state vector
%   x(:,1) - voltage (spiny stellate cells)
%   x(:,2) - voltage (pyramidal cells) +ve
%   x(:,3) - voltage (pyramidal cells) -ve
%   x(:,4) - current (spiny stellate cells)    depolarizing
%   x(:,5) - current (pyramidal cells)         depolarizing
%   x(:,6) - current (pyramidal cells)         hyperpolarizing
%   x(:,7) - voltage (inhibitory interneurons)
%   x(:,8) - current (inhibitory interneurons) depolarizing
%   x(:,9) - voltage (pyramidal cells)
%
% f        - dx(t)/dt  = f(x(t))
% J        - df(t)/dx(t)
% D        - delay operator dx(t)/dt = f(x(t - d))
%                                    = D(d)*f(x(t))
%
% Prior fixed parameter scaling [Defaults]
%
%  M.pF.E = [32 16 4];           % extrinsic rates (forward, backward, lateral)
%  M.pF.H = [1 4/5 1/4 1/4]*128; % intrinsic rates (g1, g2 g3, g4)
%  M.pF.D = [2 16];              % propogation delays (intrinsic, extrinsic)
%  M.pF.G = [4 32];              % receptor densities (excitatory, inhibitory)
%  M.pF.T = [8 16];              % synaptic constants (excitatory, inhibitory)
%  M.pF.S = [1 1/2];             % parameters of activation function
%
%__________________________________________________________________________
% David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and
% neuronal dynamics. NeuroImage 20: 1743-1755
%___________________________________________________________________________

% Karl Friston
% Copyright (C) 2005-2022 Wellcome Centre for Human Neuroimaging


% get dimensions and configure state variables
%--------------------------------------------------------------------------
x  = spm_unvec(x,M.x);      % neuronal states
n  = size(x,1);             % number of sources

% [default] fixed parameters
%--------------------------------------------------------------------------
E = [1 1/2 1/8]*32;         % extrinsic rates (forward, backward, lateral)
G = [1 4/5 1/4 1/4]*128;    % intrinsic rates (g1 g2 g3 g4)
D = [2 16];                 % propogation delays (intrinsic, extrinsic)
H = [4 32];                 % receptor densities (excitatory, inhibitory)
T = [8 16];                 % synaptic constants (excitatory, inhibitory)
R = [2 1]/3;                % parameters of static nonlinearity


    
function [f,J,Q] = spm_fx_erp(x,u,P,M)
% State equations for a neural mass model of erps
% FORMAT [f,J,D] = spm_fx_erp(x,u,P,M)
% FORMAT [f,J]   = spm_fx_erp(x,u,P,M)
% FORMAT [f]     = spm_fx_erp(x,u,P,M)
% x      - state vector
%   x(:,1) - voltage (spiny stellate cells)
%   x(:,2) - voltage (pyramidal cells) +ve
%   x(:,3) - voltage (pyramidal cells) -ve
%   x(:,4) - current (spiny stellate cells)    depolarizing
%   x(:,5) - current (pyramidal cells)         depolarizing
%   x(:,6) - current (pyramidal cells)         hyperpolarizing
%   x(:,7) - voltage (inhibitory interneurons)
%   x(:,8) - current (inhibitory interneurons) depolarizing
%   x(:,9) - voltage (pyramidal cells)
%
% f        - dx(t)/dt  = f(x(t))
% J        - df(t)/dx(t)
% D        - delay operator dx(t)/dt = f(x(t - d))
%                                    = D(d)*f(x(t))
%
% Prior fixed parameter scaling [Defaults]
%
%  M.pF.E = [32 16 4];           % extrinsic rates (forward, backward, lateral)
%  M.pF.H = [1 4/5 1/4 1/4]*128; % intrinsic rates (g1, g2 g3, g4)
%  M.pF.D = [2 16];              % propogation delays (intrinsic, extrinsic)
%  M.pF.G = [4 32];              % receptor densities (excitatory, inhibitory)
%  M.pF.T = [8 16];              % synaptic constants (excitatory, inhibitory)
%  M.pF.S = [1 1/2];             % parameters of activation function
%
%__________________________________________________________________________
% David O, Friston KJ (2003) A neural mass model for MEG/EEG: coupling and
% neuronal dynamics. NeuroImage 20: 1743-1755
%___________________________________________________________________________

% Karl Friston
% Copyright (C) 2005-2022 Wellcome Centre for Human Neuroimaging


% get dimensions and configure state variables
%--------------------------------------------------------------------------
x  = spm_unvec(x,M.x);      % neuronal states
n  = size(x,1);             % number of sources

% [default] fixed parameters
%--------------------------------------------------------------------------
E = [1 1/2 1/8]*32;         % extrinsic rates (forward, backward, lateral)
G = [1 4/5 1/4 1/4]*128;    % intrinsic rates (g1 g2 g3 g4)
D = [2 16];                 % propogation delays (intrinsic, extrinsic)
H = [4 32];                 % receptor densities (excitatory, inhibitory)
T = [8 16];                 % synaptic constants (excitatory, inhibitory)
R = [2 1]/3;                % parameters of static nonlinearity

% [specified] fixed parameters
%--------------------------------------------------------------------------
if isfield(M,'pF')
    if isfield(M.pF,'E'), E = M.pF.E; end