I am taking course on dynamical systems and I am asked to show that the growth rate of a population $N'/N=r-a(N-b)^2$ demonstrates the Allee effect if $r$, $a$, and $b$ satisfy certain constraints, which I must determine.
I came to the conclusion that $a,b,r>0$ for the effect to be demonstrated.
I would like to know if this is correct. Also, assuming it is, I used brute force testing in order to come to this conclusion and I am wondering if there is a better way of showing it.
Thanks!