function dx = modele(t,x,alpha,beta)
% This function defines the
ordinary differential equations that provide
% a large scale description of our
system.
%
% CALL: [dx] = modele(t, x,
alpha, beta)
% t = scalar value,
time
% x = vector
representing the concentrations of the genes ( 5 genes )
% alpha = parameter of a Hill
function, we will change it for robustness
%
studies.
% beta = parameter of a Hill
function, we will change it for robustness
%
studies.
% dx =
derivative of the concentrations
%
% This function uses the
following formalism dx=x'=f(x)
%
% x(1) : FlhDC
% x(2) : FliA
% x(3) : Z1
% x(4) : Z2
% x(5) : Z3
%% Parameters
n=6;
B=10;
k(1)=10;
k(2)=0.2;
k(3)=beta;
%k(3)=10;
k(5)=n;
p(4)=5;
p(5)=B;
p(6)=n;
p(7)=20;
p(8)=B;
p(9)=n;
p(10)=10;
p(11)=B;
p(12)=n;
p(13)=8;
p(14)=10;
p(15)=n;
%p(16)=20;
p(16)=alpha;
p(17)=B;
p(18)=n;
p(19)=10;
p(20)=B;
p(21)=n;
p(22)=33;
p(23)=0;
p(24)=n;
%% ODE
dx(1)=k(1)*(1-Hill(x(5),k(3),1,k(5)))-k(2)*x(1);
dx(2)=Hill(x(1),p(1),p(2),p(3))+
Hill(x(2),p(22),p(23),p(24))-k(2)*x(2);
dx(3)=Hill(x(1),p(4),p(5),p(6))+
Hill(x(2),p(7),p(8),p(9))-k(2)*x(3);
dx(4)=Hill(x(1),p(10),p(11),p(12))+
Hill(x(2),p(13),p(14),p(15))-k(2)*x(4);
dx(5)=Hill(x(1),p(16),p(17),p(18))+
Hill(x(2),p(19),p(20),p(21))-k(2)*x(5);
dx=dx(:);
"
