Consider a lake where fishing occurs at a constant rate. $N_i$ is population of fish at time point $i$ and discrete model is written in the following format: $N_{i+1} = N_i + BN_i -DN_i^2-Y$
Since it is a constant harvesting $(Y)$ effort, can I re-write this model as $N_{i+1} = N_i + BN_i -DN_i^2-YN_i$? Also, to find the steady states of the system can I set $N_{i+1} = N_i = N'$? Also, if I wanted to find the stability of this, would I just set $N_{i+1} = N_i = N'$ and differentiate the function $F[N']= N' + BN' -DN'^2-YN'$ and then sub in my steady state values to determine stability?