Description

Homework guidelines for writers:

(Adapted from the website of Professor Andy Ruina). To get full credit, please do these things on each homework.
MA 508
HW 4
On the top right corner, please put your group number, the names of your group members, with the writer at the top and clearly indicated. Also indicate any non-participating group members, e.g.:
Group 3
Sidney Crosby (writer)
Marissa Tomei
Michelle Wie
Barry Obama (did not participate)
4. Your work should be laid out neatly enough to be read by someone who does not know how to do theproblem. For most jobs, it is not sufficient to know how to do a problem, you must convince others that you know how to do it. Your job on the homework is to practice this. Box your answers.
This homework covers 1. Classification of fixed points (2+D); 2. Linearization (2+D); 3. 2D phase portraits near a fixed point.
These topic are covered in §5.0-6.3 in Strogatz.

Part of getting good at drawing phase portraits is experience. Here are four relatively simple systems (all from the book) to help you practice.

For each of the following (problems 1-3):
a) Find all fixed points and classify them;
b) Sketch the local phase portrait near each fixed point.

1.
x˙ = 1 + y−e−x y˙ = x3−y
2.
x˙ = xy− 1 y˙ = x−y3
3.
x˙ = x(3 −x−y) y˙ = y(2 −x−y)