Exercise 31

Consider the following predator-prey systems of differential equations $$\begin{aligned} \frac{dx}{dt} & = -\frac{x}{2} + \frac{xy}{2 + y}, \\ \frac{dy}{dt} &= y(1 - y) - \frac{xy}{2 + y}. \end{aligned}$$

1. Which equation models the prey population and which equation models the predator population?

2. How does the prey population grow if there are no predators present?

3. What happens if there are a lot of prey present?