function [ dSdt ] = chemostat_dynamics(t,S)
% this function defines the chemostat differential equation
global rM K d eps

dSdt = zeros(size(S));

x = S(1); % cells
y = S(2); % food

ry = rM*y/(K+y);

dxdt = (ry-d)*x;

dydt  = -eps*ry*x;

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

end