Homework 

Chapter

Problems

Date due

1

Strogatz: 2 and 3

Wed, Jan 21

2

Strogatz: 3 and 5

3.4.1, 3.4.7, 3.4.8, 

5.2.6, 5.2.8, 5.2.13

google: find another (bistable) system that exhibits hysteresis (briefly describe the hysteresis + figure + reference)

Wed, Jan 28

3

Strogatz: 5, 6, 10 

5.3.2

6.1.1, 6.1.5 (include null clines in discussion)

Computer problem:

A) numerically integrate the simple harmonic oscillator:  generate one phase space figure, where you plot at least three trajectories with different initial conditions. 

B) numerically integrate the Van der Pol oscillator [Eq. (2)  in chapt. 7]: generate one phase space figure, where you plot at least three trajectories with different initial conditions. 

C) discuss the difference between A) and B) 

10.1.4

Wed, Feb 4

4

Strogatz:

6, 10, 11

6.4.1

10.1.10 (do it both ways, graphically and analytically)

10.2.4-10.2.8: pick two problems, rest for fun if you like

10.5.1 + interpret result, 

10.5.6 (also do the orbit diagram and compare with lyapunov exponent), 

11.3.1, 

11.3.8 

google: find another system (whatever the scientific discipline) that exhibits a period doubling scenario (into chaos).  briefly describe the behavior + figure + reference

Fri, Feb 13