error in using the function fsolve to find steady state

I am new to programming. I have a mini project on the Lokta- Volterra model. one of the point is to find the steady state of the model. I have used the fsolve function however i receive the error "'fsolve' requires optimisation toolbox" not sure what it mean. the code is as follow can some one help me seeing my mistake?

% Symbolic solution of the steady state equations

syms x1 x2 k1 k2 k3

[x1_ss, x2_ss] = solve(k1*x1 - k2*x1*x2==0, k2*x1*x2 - k3*x2==0 )

% numerical steady states

k1 = 1.1; k2 = 0.001; k3 = 10;

F = @(x) [k1*x(1) - k2*x(1)*x(2), k2*x(1)*x(2) - k3*x(2)];

XO =[15000, 1000];

F_ss = fsolve(F, XO)

thank you

[David Hill]

Requires optimization toolbox which is not part of basic MATLAB

https://www.mathworks.com/products/optimization.html

[Sara Vasciaveo]

oh so I need to dowloaded?! ok thanks

[Sara Vasciaveo]

as it seems I have trouble downloading is there another way to achieve the same withouth the toolbox?

Answer 1

[Alan Stevens]

Using the Optimization toolbox to solve these equations seems like using a sledgehammer to crack a nut!

It is clear from the equations that the non-trivial solution is x1 = k3/k2 and x2 = k1/k2.

(There is also the trivial solution x1 = x2 = 0).

[Sara Vasciaveo]

great thank yu so much !!

Answer 2

[Steven Lord]

Don't try using a numeric solver like fsolve on a function that returns symbolic answers. Use the solve function from Symbolic Math Toolbox, which can operate on symbolic expressions, instead.