Nondimensionalization of given equation

Question

I have the following equation, which is a logistic system with a death term, $$\frac{dN}{dt}=rN(1-N/k)-p(N),$$ where $p(N)=\frac{BN^2}{A^2+N^2},$ for unknown constans $A,B$. I want to nondimensionalice the equation with a change of variables. I tried the typical change of variables for the nondimensionalization of the simple logistic equation, but i'm not being able to manage with $A$ and $B$. Any help will be very appreciated!