Chapter 2.1, Problem 4E

Exercises 1-6 refer to the following systems of equations:

(i) $\begin{array}{l}\frac{dx}{dt}=10x\left(1-\frac{x}{10}\right)-20xy\\ \frac{dy}{dt}=-5y+\frac{xy}{20}\end{array}$

  (ii) $\begin{array}{l}\frac{dx}{dt}=0.3x-\frac{xy}{100}\\ \frac{dy}{dt}=15y\left(1-\frac{y}{50}\right)+25xy\end{array}$

4. For each system, describe the behavior of the prey population if the predators are extinct. (Sketch the phase line for the prey population assuming that the predators are extinct, and sketch the graphs of the prey population as a function of time for several solutions. Then interpret these graphs for the prey population.)