The following system of ODEs – is it recognized as distinct system, with meaningful background and uses?
$$\frac{dx}{dt} = - [x(t)]^2 - x(t)y(t)$$ $$\frac{dy}{dt} = - [y(t)]^2 - x(t)y(t)$$
This is probably not needed, but initial conditions: $x(t=0) = x_0, \space y(t=0) = y_0$