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ReducedHMR.m
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ReducedHMR.m
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%% Implements Equation 3 (Reduced system of HMR) from (see ./docs):
% Stefanescu RA, Jirsa VK (2008), Neurons. PLoS Comput Biol 4(11).
% "A Low Dimensional Description of Globally Coupled Heterogeneous Neural
% Networks of Excitatory and Inhibitory".
%
%
% ARGUMENTS:
% x(NumberOfModes,NumberOfNodes) -- State variable Xi
% y(NumberOfModes,NumberOfNodes) -- State variable Eta
% z(NumberOfModes,NumberOfNodes) -- State variable Tau
% w(NumberOfModes,NumberOfNodes) -- State variable Alpha
% v(NumberOfModes,NumberOfNodes) -- State variable Beta
% u(NumberOfModes,NumberOfNodes) -- State variable Gamma
% P -- Structure containing parameters
% .A(NumberOfModes,NumberOfModes) --
% .B(NumberOfModes,NumberOfModes) --
% .C(NumberOfModes,NumberOfModes) --
% .a_i(NumberOfModes,NumberOfNodes) --
% .e_i(NumberOfModes,NumberOfNodes) --
% .b_i(NumberOfModes,NumberOfNodes) --
% .f_i(NumberOfModes,NumberOfNodes) --
% .c_i(NumberOfModes,NumberOfNodes) --
% .h_i(NumberOfModes,NumberOfNodes) --
% .IE_i(NumberOfModes,NumberOfNodes) --
% .II_i(NumberOfModes,NumberOfNodes) --
% .d_i(NumberOfModes,NumberOfNodes) --
% .p_i(NumberOfModes,NumberOfNodes) --
% .m_i(NumberOfModes,NumberOfNodes) --
% .n_i(NumberOfModes,NumberOfNodes) --
% .r --
% .s --
% .K11 -- Excitatory to excitatory coupling.
% .K12 -- Excitatory to inhibitory coupling.
% .K21 -- Inhibitory to excitatory coupling.
%
% OUTPUT:
% Fx(NumberOfModes,NumberOfNodes) -- Derivative of state variable Xi
% Fy(NumberOfModes,NumberOfNodes) -- Derivative of state variable Eta
% Fz(NumberOfModes,NumberOfNodes) -- Derivative of state variable Tau
% Fw(NumberOfModes,NumberOfNodes) -- Derivative of state variable Alpha
% Fv(NumberOfModes,NumberOfNodes) -- Derivative of state variable Beta
% Fu(NumberOfModes,NumberOfNodes) -- Derivative of state variable Gamma
%
% USAGE:
%{
<example-commands-to-make-this-function-run>
%}
%
% MODIFICATION HISTORY:
% SAK(24-11-2009) -- Original.
% SAK(Nov 2013) -- Move to git, future modification history is
% there...
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Fx Fy Fz Fw Fv Fu] = ReducedHMR(x, y, z, w, v, u, P)
Fx = y - P.a_i.*x.^3 + P.b_i.*x.^2 - z + P.K11.*(P.A*x - x) - P.K12.*(P.B*w - x) + P.IE_i;
Fy = P.c_i - P.d_i.*x.^2 - y;
Fz = P.r.*P.s.*x - P.r.*z - P.m_i;
Fw = v - P.e_i.*w.^3 + P.f_i.*w.^2 - u + P.K21.*(P.C*x - w) + P.II_i;
Fv = P.h_i - P.p_i.*w.^2 - v;
Fu = P.r.*P.s.*w - P.r.*u - P.n_i;
end % function ReducedHMR()