[Solved] MA508 Homework 4

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):

1. Find all fixed points and classify them;
2. Sketch the local phase portrait near each fixed point.

1.

x = 1 + ye^x y = x³y

2.

x = xy 1 y = xy³

3.

x = x(3 xy) y = y(2 xy)