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Classification of fixed points (2+D)

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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˙ = x
3 − y
2.
x˙ = xy − 1
y˙ = x − y
3
3.
x˙ = x(3 − x − y)
y˙ = y(2 − x − y)
4. Turn in a completed version of worksheet 4, which you worked on during class on September 22.
3

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