For a logistic population model with a harvest parameter H,
\frac{dN}{dt} = f(N) = N\left(1 - \frac{N}{K}\right) - H
Please perform qualitative analysis and show
i. If H > 0.25K, f(N) < 0, i.e., there is no equilibrium points, and for any initial
population, the population becomes extinct in finite time.
ii. For 0 < H < 0.25K, there are two equilibrium points, one is stable and the other is unstable.