I have the system below. It is used to model the interaction between predator and prey.
$$x' = x-xy, y' = -y + xy$$
The solution curves are closed contours about the point $(1,1)$. I determined this by using that along any solution curve $$\frac{d(xe^{-x}ye^{-y})}{dt} = 0$$ (The above might be useful???)
"Briefly explain why the behaviour of each population separately cannot be described by a single autonomous differential equation"
I do not know what to say. Is it because each population separately would be periodic in nature? we can prove that we can not model oscillatory behaviour with autonomous differential equations fairly easily. I feel like I am falling into a pit here though.