Trouble finding equilibria of nonlinear system of equations

I am trying to find the equilibria of the system:

• x' = x( 1 - x - y - z) - (x/G_x)
• y' = F_y * [ y * (1 - x - y - z) - (y/G_y) + x * U]
• z' = F_z * [ z * (1 - x - y - z) - (z/G_z) + y * W]

where G_x, G_y, G_z, F_y , F_z, U, and W should be treated like unknown parameters. I have the following in an m-file:

function fcns = eqns(a)
    x = a(1);
    y = a(2);
    z = a(3);
    fcns(1) = x( 1 - x - y - z) - (x/G_x);
    fcns(2) = F_y * ( y * (1 - x - y - z) - (y/G_y) + x * U);
    fcns(3) = F_z * [ z * (1 - x - y - z) - (z/G_z) + y * W];
end

I want to find the equilibria of the system (or zeros) so I use the fsolve(@eqns) function, but I get an error. Could any of you provide me with some assistance?

EDIT: The first error I got was "The input to FSOLVE should be either a structure with valid fields or consist of at least two arguments." So I added the argument x...

fsolve(@eqns, x)
Undefined function or variable 'x'.

I have x defined in the m-file though.

Answer 1

[Star Strider]

I am guessing that the error is ‘not enough input arguments’ if you are calling fsolve as you mentioned. The fsolve function requires an initial estimate of the parameters as its second input.

If that is not the error you are getting, please post the part of your code that generates the error, and include the complete error message.

[Anthony]

I have updated my question with the error that I am getting. I guess I should not be using the fsolve function since I cannot estimate my parameters.

[Star Strider]

I don’t know what ‘x’ is either. I suggest you change part of your code to:

a0 = ones(3,1);
[a, fval]  = fsolve(@eqns, a0)

and see what that result is. The a vector is x, y, and z as you have defined them, and fval is the value of the function at the solution.