Math 134 - Homework 5 Solution

1. (Based on Strogatz Exercise 3.6.2) Consider the system x = h + rx x2. When h = 0, this system undergoes a transcritical bifurcation at r = 0.


        (a) Sketch the bifurcation diagram of x against r for h < 0, h = 0, and h > 0.

        (b) Sketch the bifurcation diagram of x against h for r < 0, r = 0, and r > 0.

    2. Problem 3.5.8 in Strogatz.

    3. Problems 4.3.3, 4.3.6, 4.3.4, 4.1.3, 4.1.5 and 4.1.6. We will cover the material needed to solve these problems by Wednesday.