function [ dSdt ] = chemostat(t,S)
% this function defines the chemostat differential equation
global q u r K V
dSdt = zeros(size(S));

c = S(1);
y = S(2);

dcdt = q*u - q*c -((y*c*V)/(K+c));

dydt = (y*r)*(V*c)/(K+c) - q*y;

dSdt(1) = dcdt;
dSdt(2) = dydt;

end