University of Toronto at Mississauga
Spring 2010

Course Outline
MAT 332H5S, Introduction to Nonlinear Dynamics and Chaos

Instructor: Michael Yampolsky, Room SE4061
e-mail: yampol@math.utoronto.ca
Lectures: Tuesdays 3pm-4pm, and Thursdays 4pm-6pm, Room CC3150
Office hours: Tuesdays 11:30-12:30, Thursdays 11:30-12:30 or by appointment
TA: Alex Shlakhter, oleksandr.shlakhter@utoronto.ca
Tutorial sessions: Mondays 12-1pm, Room SE1154 Office hours: Mondays 11-12, Room SE4061
Textbook: An Introduction to Nonlinear Systems, Continuous and Discrete, by Clark Robinson. 1st Edition, Pearson Education, 2004.
Other suggested reading. The following books are not required for the course. You may, however, find them interesting and useful: Devaney, "A first course in chaotic dynamical systems", and "Introduction to chaotic dynamical systems"; Lynch "Dynamical systems with applications using MAPLE"; Strogatz "Nonlinear dynamics and chaos. With applications to physics, biology, chemistry, and engineering".
Computing projects: The computational side of the course will be based on the use of a powerful computer algebra system Maple. Please click here for the links to Maple resources. The author of the textbook also has some sample Maple worksheets on his web page.
Web Page: http://www.math.utoronto.ca/~yampol/MAT332Spring2010.html

Marking scheme:

40% bi-weekly take home assignments.
20% Midterm, March 2, in class
40% Final Exam

IMPORTANT: Please note that there will be no make-up tests, an undocumented absence will result in zero credit. No late assignments will be accepted. A late hand-in will also result in zero credit.

Click here for assignment 4. Due March 16.

Click here for assignment 5. Due April 1.

Click here for the suggested homework exercises.

Supporting materials.

Click here for the supporting materials for Chapter 1: numerical study of linear and nonlinear oscillators; examples of chaos: double pendulum, forced simple pendulum.
Right-click here to save a Maple worksheet with examples of linear systems with constant coefficients for Chapter 2.
Right-click here to save a Maple worksheet with examples of linear systems with quasi-periodic solutions (Chapter 2). Here is a Java simulation of a double spring from myphysicslab.com.
Right-click here to save a Maple worksheet with examples of limit sets (Chapter 4).
Right-click here to save a Maple worksheet with examples of phase portrait study of nonlinear systems in 2D (Chapter 4).
Right-click here to save a Maple worksheet with examples of phase portrait study of nonlinear systems using energy-type functions (Chapter 5).
Right-click here to save a worksheet with an example of a gradient flow (Chapter 5).
Right-click here to save a Maple worksheet explaining why a saddle is called a "saddle"
Right-click here to save a worksheet with a study of periodic orbits (Chapter 6).
Right-click here to save a worksheet with examples of oscillating chemical reactions (Chapter 6)
Right-click here to save a worksheet with an example of a Lienard system (Chapter 6).
Right-click here to save a worksheet with examples of bifurcations in 2D phase portraits (Chapter 6).
Right-click here to save a worksheet with examples of predator-prey systems (Chapter 6).
Right-click here to save a worksheet with examples of a Poincare map in a 2D system (Chapter 6).
Right-click here to save a worksheet with a study of chaos in the Lorenz system (Chapter 7).
Another example of chaos -- forced nonlinear oscillator. The worksheet includes the study of the Poincare map (Chapter 7).
Right-click here to save a worksheet with examples of graphical iteration (Chapters 8 and 9).
Click here to see a Java simulation of the iterated logistic map. This Java applet was kindly made available to the Web community by A. Burbanks http://www.maths.bris.ac.uk/~maadb/