Do Lab 3.1 in the text. (This is on page 341.)

While this lab is purely analytic, requiring no numerical approximations to answer the questions, you may find MATLAB useful for checking your solutions, as well as producing illustrations for your report. Recall, however, the warning from the authors:

`... although one good illustration may be worth 1000 words, 1000 illustrations are usually worth nothing.'

If you feel tempted to include a large number of illustrations, analyze why, and see if you can say in words what you hope I would get from the illustrations. Then select a limited number of important examples.

In question 2, at each of the five bifurcations which can occur, describe the nature of systems near the bifurcation on either side, as well as answering the book's questions:

• Which of the bifurcations corresponds to a change in the long term behavior of solutions?
• Which of the bifurcations corresponds to a dramatic change in either the trajectories in the phase plane, or the graphs of x(t) or y(t) against time?