Chapter 16.4, Problem 14E

(a)

To determine

To sketch: The phase line and also to discuss the reasonableness of the given model $\frac{dP}{dt}=rP\left(M-P\right)\left(P-m\right)$ for the growth rate of the deer population.

(b)

To determine

The way in which the model differs from the logistic model $\frac{dP}{dt}=rP\left(M-P\right)$ and also to determine whether is it more or less reasonable than the logistic model.

(c)

To determine

To show: The value of $\underset{t\to \infty }{\lim }P\left(t\right)=M$, if $P>M$ for all t.

(d)

To determine

The consequences if $P<m$ for all t.

(e)

To determine

The solutions to the differential equation, the equilibrium points of the model, the dependence of the steady state value of P on the initial values of $P$ and also to determine the number of permits to be issued.