Attractors, Repellers, and Periodic Points

Math 480, Section 5618, Summer 2004

MTWRF, Ivers 210


Professor: Dr. Douglas Anderson
  Ivers 234G
  299-4453
  andersod

Texts: A First Course in Discrete Dynamical Systems, Second Edition, by Richard A. Holmgren (Springer, 1996); Does God Play Dice? The Mathematics of Chaos, Second Edition, by Ian Stewart (Blackwell, 2002). A reference text is Discrete Dynamical Systems and Difference Equations with Mathematica, by Mustafa R.S. Kulenovic and Orlando Merino (Chapman & Hall/CRC, 2002).

Dynamica: To download into Mathematica the extra package Dynamica, go to the download Dynamica website at the University of Rhode Island. Save it in Program Files > Wolfram > Mathematica > 5.0 > AddOns > ExtraPackages. Once it is in ExtraPackages, unzip it and put the file Dynamica.m directly in the ExtraPackages folder, outside of the Dynamica subfolder.


Daily Schedule, with Assignments:
      
Date Notebook Exercises
May 24 Iterated Maps (7) 1.1, 1.3, 1.5, 1.6
25 Logistic Equation (17) 2.1, 2.3, 2.4, 2.5, 2.8, 2.9, 2.11, 2.15, 2.16, 2.17, 2.18, 2.19, 2.20
      
31 Staircase Diagram (28) 3.1, 3.4, 3.6, 3.11, 3.13, 3.14, 3.15
June 1 Tent Map (38) 4.1, 4.2, 4.3, 4.5, 4.7, 4.9, 4.10
2 Period 3 (45) 5.2, 5.3, 5.5
3 Nonhyperbolic Case (54) 6.1, 6.2, 6.4, 6.7
4 Bifurcations (67) 7.1, 7.2
      
7 Bifurcation Diagrams (84) 8.2, 8.3, 8.5
8 Cantor Sets (92) 9.3, 9.5
      
21 Chapter 10 (107) 10.6, 10.9
22 Symbolic Dynamics (123) 11.6, 11.9, 11.15
23 Newton's Method Read Section 12.2
24 Newton's Method (148) 12.5, 12.6
25 Newton's Method (149) 12.8, 12.9, 12.11, 12.12, 12.13
      
28 2D Phase Portrait Handout 1-7
29 2D Predator-Prey Model
30 Manifolds
July 1 Henon's Map
2 Cournot Duopoly
      
6 Duopoly Dynamics
7 Newton code
8 Basins of Attraction
9 Basin Points
      
12 Rectangles
15 Circles!
      
21 Basins for any A,B
      
Oct 28 Power Point
28b Animation Period Double: y=x
28c Phase Portrait
28d Basin Pictures


  • Concordia College home page.
  • Douglas Anderson's home page.

  • Last modified: 28 October 2004