Introduction

We use Maple's DEtools to study solutions of the Lotka-Volterra system and its refinements as described in sections 1.1 and 2.1 of the BDH text As you play with the models, keep these questions in mind:

Points to Ponder

The following five questions should be answered for each system considered in this worksheet.

1. What is the long term behavior of the system?

2. In the case of oscillations, what is the period (time interval from peak to peak or trough to trough), and what is the amplitude?

3. How does changing the initial conditions affect your answers to qustions 1 and 2?

4. Does the system have any steady states (equilibria)? Do these appear to be stable or unstable?

5. If there are steady states, are they in any way related to the long term behavior?

>

We first consider a model similar to the one on page 140 of the text.. Here represents the rabbit population and represents 60 times the fox population (since the fox population is numerically much smaller than the rabbit population, we scale it up to fit on the same graph).

> restart:

> with(plots):

> with(DEtools):

>