Just a quick question I have the following system: $\frac{dx}{dt}=x\left(2-x-\frac{y}{1+x}\right),\qquad \frac{dy}{dt}=3y\left(\frac{x}{1+x}-4y\right)$ It asks which variable represents the predator and which the prey, write down the long term size of the prey in the absence of predators.
I approached this by considering that $\frac{dy}{dx}= \frac{y(3x-12y-12yx)}{x(2+x-x^{2}-y)}$, hence when y=o we have that $\frac{dy}{dx}$=0 and therefore we have that our predator is represented by $\frac{dx}{dt}$ and prey by $\frac{dy}{dt}$. Additionally in the absence of prey our prey will tend to $\infty$.
Many thanks in advance.