Chapter 2.1, Problem 1E

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

1. In one of these systems, the prey are very large animals and the predators are very small animals, such as elephants and mosquitoes. Thus it takes many predators to cat one prey, but each prey eaten is a tremendous benefit for the predator population. The other system has very large predators and very small prey. Determine which system is which and provide a justification for your answer.