Solving a system with for loop

I would like to solve a system of equations using a for loop and plotting the data.

This is my system

function f = Thesissysteem(x,parameters)

thethaA1= parameters(1);
thethaA2= parameters(2);
thethaN1= parameters(3);
thethaN2= parameters(4);
ebar    = parameters(5);
alpha1  = parameters(6);
alpha2  = parameters(7);
sigma   = parameters(8);
B       = parameters(9);
cap     = parameters(10);
tax     = parameters(11)

f(1)= x(1) - B * x(11).^thethaA1;
f(2)= x(2) - B * x(12).^thethaA2;
f(3)= x(3) - B * x(13).^thethaN1;
f(4)= x(4) - B * x(14).^thethaN2;
f(5)= 1 * (x(1)-x(5))+ x(17) * (x(2)-x(6))-x(18) * x(11)-x(19) * x(12);
f(6)= 1 * (x(3)-x(7))+ x(17) * (x(4)-x(8))-x(18) * x(13)-x(19) * x(14);
%f(7)= 1 * thethaA1 * B * x(11).^(thethaA1-1) - x(18);
f(7)= x(11) - cap
f(8)= x(17) * thethaA2 * B * x(12).^(thethaA2-1) - x(19);
f(9)= 1 * thethaN1 * B * x(13).^(thethaN1-1) - x(18);
f(10)= x(17) * thethaN2 * B * x(14).^(thethaN2-1) - x(19);
f(11)= (alpha1 / alpha2) * (x(5) / x(6)).^ (-1 / sigma) - (1 / x(17));
%f(11)= (alpha1 / alpha2) * (x(5) / x(6)).^ (-1 / sigma) - (1 + tax / x(17))
f(12)= (alpha1 / alpha2) * (x(7) / x(8)).^ (-1 / sigma) - (1 / x(17));
f(13)= (alpha1 / alpha2) * (x(9) / x(10)).^ (-1 / sigma) - (1 / x(17));
f(14)= x(1) + x(3) - x(5) - x(7) - x(9);
f(15)= x(2) + x(4) - x(6) - x(8) - x(10);
f(16)= x(15) - x(11) - x(13);
f(17)= x(16) - x(12) - x(14);
f(18)= ebar - x(15) - x(16);
f(19)= x(18) - x(19);

With the following values for the parameters

thethaA1= 0.05;
thethaA2= 0.05;
thethaN1= 0.05;
thethaN2= 0.05;
ebar    = 1;
alpha1  = 1.5631;
alpha2  = 1;
sigma   = 0.5;
B       = 1.191; 
cap     = 0;
tax     = 0;

I want to find values for x(11) with different values for sigma (0<sigma<1) with steps of 0.1.

thethaA1= 0.05;
thethaA2= 0.05;
thethaN1= 0.05;
thethaN2= 0.05;
ebar    = 1;
alpha1  = 1.5631;
alpha2  = 1;
sigma   = 0.3;
B       = 1.191; 
cap     = 0;
tax     = 0;


parameters = [thethaA1 thethaA2 thethaN1 thethaN2 ebar alpha1 alpha2 sigma B cap tax];

for i =  0:0.1:1  
    parameters = [thethaA1 thethaA2 thethaN1 thethaN2 ebar alpha1 alpha2 sigma B cap tax];
    
    [t1, x(11)] = Thesissysteem(parameters, i);
end 
   

Is this the correct way to create such a loop? I get the following error:

Error using Thesissysteem
Too many output arguments.

Error in untitled2 (line 20)
    [t1, x(11)] = Thesissysteem(parameters, i);

Can someone help me please?

[Torsten]

x(11) will always be equal to cap, independent of sigma.

[Jolijn Pruijmboom]

sorry I forgot to change that

f(7) has to be the function with % instead of f(7)= x(11) - cap

[Torsten]

And where is your call to the nonlinear solver that you use to solve your system ?

[Jolijn Pruijmboom]

clear;
clc;

thethaA1= 0.05;
thethaA2= 0.05;
thethaN1= 0.05;
thethaN2= 0.05;
ebar    = 1;
alpha1  = 1.5631;
alpha2  = 1;
sigma   = 0.5;
B       = 1.191; 
cap     = 0;
tax     = 0;
 
parameters = [thethaA1 thethaA2 thethaN1 thethaN2 ebar alpha1 alpha2 sigma B cap tax];

guess = [ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1];

[solution, fval, eflag, out] = fsolve(@(x) Thesissysteem(x,parameters),(guess),...
 optimset('TolX',1.0e-8,'TolFun',1.0e-8,'MaxFunEvals',100000,'MaxIter', 100000));

I use this to solve the system!

[Torsten]

Then call fsolve in a loop:

sigma_array = [0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9];

for i=1:numel(sigma_array)

sigma = sigma_array(i);

parameters(8) = sigma;

% your call to fsolve

solution_array(i,:) = solution; % maybe to be changed to solution_array(:,i) = solution if solution is a column vector

end