Chapter 2.1, Problem 2E

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

2. Find all equilibrium points for the two systems. Explain the significance of these points in terms of the predator and prey populations.