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):
- Find all fixed points and classify them;
- 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)
