Chapter 9.6, Problem 11E

In Example 1 we used Lotka-Volterra equations to model populations of rabbits and wolves. Let’s modify those equations as follows:

$\begin{array}{l}\frac{dR}{dt}=0.08R(1-0.0002R)-0.001RW\hfill \\ \frac{dW}{dt}=-0.02W+0.00002RW\hfill \end{array}$

1. (a) According to these equations, what happens to the rabbit population in the absence of wolves?
2. (b) Find all the equilibrium solutions and explain their significance.
3. (c) The figure shows the phase trajectory that starts at the point (1000, 40). Describe what eventually happens to the rabbit and wolf populations.

1. (d) Sketch graphs of the rabbit and wolf populations as functions of time.