Growth kinetics ODE 15

I am trying to simulate a growth kinetics experience however I am constantly getting this error for my functions, any idea of how to solve it? I attached the function, script and error. Thank you!

function dx=odesys(t,x,var)
var[]

%Rate equations 
l=0.001;
Io=125e-6;
Il=Io*exp(-sigma*x*l);
mux=mumax*(x(3)/(x(3)+Kxs+((x(3)).^2)/Kixs))*(x(4)/(x(4)+Kxn+((x(4)).^2)/Kixn))*(Il/(Il+Kxl+(Il.^2/Kixl)));
mul=qlmax*(x(3)/(x(3)+Kls+((x(3)).^2)/Kils))*(Kinl/(x(4)+Kinl)*(Il/(Il+Kli+(Il.^2/Kili))));

%ODE
dx(1)=mux.*x(1);
dx(2)=mul.*x(1);
dx(3)=(-(1/Yxs)*dx(1))-((1/Yls)*dx(2));
dx(4)=(-(1/Yxn)*dx(1));
dx(5)=(k1*(x(3)/(x(3)+Kgas))*(x(4)/(x(4)+Kgan+((x(4)).^2))/Kigan));
dx(6)=(k2*(x(3)/x(3)+Kfas)*(x(4)/x(4)+Kfan));
dx(7)=-Kh*(dx(3));

% The function return value is always a vector length equal to number of
% equations in model, and has to be a column vector

dx=dx';
end 

Script:

clear all
clc
int=[0.001;0;2.1;0.098;0;0;7];
%Time span to solve ODE
tspan=[0 120];
options=[];
var=[0.227;0.050;9.923;0.065;0.5;0.121;6.554;0.110;380.023;1.47;6.883;0.879;0.064;19.519e-6;2053.924e-6;15.023e-6;2152.918e-6;34.104;0.329;1.456;12.976;2.533;1.4055;12.976;2.533];
%Using ODE 15 to solve system
[t,X]=ode15s(@odesys,tspan,int,options,var);

Errors:

    Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.

Error in odesys (line 46)
dx(1)=mux.*x(1);

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:});   % ODE15I sets args{1} to yp0.

Error in ode15s (line 150)
    odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in script (line 14)
[t,X]=ode15s(@odesys,tspan,int,options,var);

Answer 1

[Star Strider]

The problem is here:

Il=Io*exp(-sigma*x*l);

since ‘x’ (and therefore ‘Il’) is a (7x1) vector, and it creates the right-hand-side of ‘mux’ as:

         0    0.0812         0         0         0         0         0
         0    0.0812         0         0         0         0         0
         0    0.0756         0         0         0         0         0
         0    0.0809         0         0         0         0         0
         0    0.0812         0         0         0         0         0
         0    0.0812         0         0         0         0         0
         0    0.0640         0         0         0         0         0

that is clearly not the scalar result you apparently want.

You need to decide on how you want to fix that.

.

[Carmen Escalante]

How could I fix it? thank you

[Star Strider]

As always, my pleasure!

‘How could I fix it?’

I cannot determine that because I do not know what you want to do, or the system you are modeling. You need to decide what you want ‘Il’ to be. If you attach a PDF describing the system you want to simulate, I will see if I can determine how to fix it.

[Carmen Escalante]

Following the initial conditions and var constants that are given in the code this is the set of equations I am trying to model a system with 7 state variables and ODEs for the modelling of microalgael growth I am modelling an already existing paper to gain more knowledge on growth kinetics.

[Star Strider]

The PDF solves the mystery!

The calculation for ‘Il’ should be:

Il=Io*exp(-sigma*x(1)*l);

since the reference to ‘X’ in the PDF is actually ‘x(1)’ in your code. With that change, the code runs without error. The plots show what I would expect the reaction kinetics to look like.

[Carmen Escalante]

I just changed it and runs perfect thanks so much for your help!

[Star Strider]

As always, my pleasure!