June 4, 1999

INTRODUCTION TO
NONLINEAR DYNAMICS AND CHAOS
  

Physics D60-0  Spring quarter 1999 
TTh 2:30-4:00 Tech M120  Predrag Cvitanovic'
Course schedule
www.phys.nwu.edu/~predrag/NUcourses/D60-sched99.html
Course description
www.phys.nwu.edu/~predrag/NUcourses/D60-Spr99.html
Project descriptions
www.nbi.dk/ChaosBook/projects/
Related courses, software
www.nbi.dk/ChaosBook/courses/OtherCourses.html

TEXT:  Steven H. Strogatz: Nonlinear Dynamics and Chaos (Addison-Wesley 1994). All chapter and exercise numbers refer to this book, unless stated otherwise.
Some material and problem sets from Classical and Quantum Chaos webbook, available on www.nbi.dk/ChaosBook/

For people following the course, check the e-mail list. Please subscribe to the course e-mail distribution - send e-mail with text (and no header):

To: info@complex.nbi.dk
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PLACE AND TIMES:TTh 2:30 - 4:00 in Tech M120


TEACHING ASSISTANT: Yueheng Lan, Tech F321, tel. 497-3419, y-lan@nwu.edu.
Please deliver solutions to problem sets by Tuesday, at the lecture, or place them in Yueheng's mailbox, Physics and Astronomy Department mailroom Tech F223.

Lecture 1          2:30 - 4:00 tuesday, March 30, 1999 in Tech M120
Preview; Basic properties of differential equations
A brief historical introduction to the subject.
Reading: chapter 1; chapter 2, sections 2.1-2.3
Optional reading: Historical appendix of the webbook might be amusing reading.
Problems: 2.1.1, 2.1.2, 2.1.3, 2.2.7, 2.2.11

Lecture 2          2:30 - 4:00 thursday, April 1, 1999 in Tech M120
One-dimensional dynamics; Bifurcations
Reading: chapter 2, chapter 3, sections 3.0-3.3
Optional reading: Sect 4.1 of the webbook, for a more abstract definition of dynamical systems.
Problems: 2.4.7, 2.6.1, 2.7.3, 2.8.6

Lecture 3          2:30 - 4:00 tuesday, April 6, 1999 in Tech M120
Bifurcations
Reading: all of chapter 3
Problems: 3.1.2, 3.1.3, 3.2.2, 3.4.4, 3.5.4, 3.6.5

Lecture 4          2:30 - 4:00 thursday, April 8, 1999 in Tech M120
Bifurcations
Reading: chapter 3

Lecture 5          2:30 - 4:00 tuesday, April 13, 1999 in Tech M120
Flows on the circle
Reading: chapter 4, sections 4.0-4.4
Problems: 4.1.2, 4.3.1, 4.3.2

Lecture 6          2:30 - 4:00 thursday, April 15, 1999 in Tech M120
Two-dimensional systems
Reading: Chapter 5
Problems: 5.1.1, 5.1.9, 5.2.1, 5.2.6, 5.2.13

Lecture 7          2:30 - 4:00 tuesday, April 20, 1999 in Tech M120
Conservative systems and index theory
Reading: chapter 6
Problems: 6.1.2, 6.1.10, 6.3.2, 6.3.10, 6.5.8-10, 6.5.19

Lecture 8          2:30 - 4:00 thursday, April 22, 1999 in Tech M120
Conservative systems and index theory
Reading: chapter 7
Problems: 7.1.9, 7.2.9

Lecture 9          2:30 - 4:00 tuesday, April 27, 1999 in Tech M120
Poincaré-Bendixson theorem
Reading: chapter 7
Problems: 7.3.1

Lecture 10         2:30 - 4:00 thursday, April 29, 1999 in Tech M120
Non-linear oscillators and averaging
Reading: chapter 7
Problems: 7.5.3, 7.6.13

Lecture 11         2:30 - 4:00 tuesday, May 4, 1999 in Tech M120
Bifurcations in two-dimensional systems
Reading: chapter 8
Problems: 8.1.4, 8.1.11, 8.2.1, 8.2.5

Lecture 12         2:30 - 4:00 thursday, May 6, 1999 in Tech M120
Bifurcations in two-dimensional systems
Reading: chapter 8
Optional reading (not required in the course): the damped driven pendulum, Tomas Bohr's notes.
Problems: 8.3.1, 8.7.3

Lecture 13         2:30 - 4:00 tuesday, May 11, 1999 in Tech M120
Lorenz equations
Reading: chapter 9, sections 9.0, 9.2
Why Dame Mary L. Cartwright discovered chaos in 1940's.
Problems: 9.2.2, 9.2.4, 9.2.6, 9.4.2 (J.M.: 9.1.4, 9.2.2)

Lecture 14         2:30 - 4:00 thursday, May 13, 1999 in Tech M120
Lorenz system, one-dimensional maps
Reading: chapter 9, sections 9.3-9.5; chapter 10, sections 10.0-10.4
Optional reading: Sect 4.2 of the webbook, stability/Jacobinas of flows.
Problems: 9.2.4, 9.3.9, 9.4.2, 10.1.9
Projects: the current term projects are listed on www.nbi.dk/ChaosBook/projects/; please get in touch with me soon if you have a project proposal.
Final exam: current plan is to give you a small project-length problem Friday morning June 4. The problem would involve analysis of a dynamical system (fixed points, stability, bifurcations) and numerical experimentation with integration of a set of differential equations describing the system. Due date would be 2:30 PM June 8, 1999, my office.

Lecture 15         2:30 - 4:00 tuesday, May 18, 1999 in Tech M120
One-dimensional maps
Reading: chapter 10, sections 10.5-10.7
Problems: 10.1.12, 10.1.13, 10.2.6, 10.4.5

Lecture 16         2:30 - 4:00 thursday, May 20, 1999 in Tech M120
Renormalization theory; fractals
Reading: chapter 10, sections 10.6-10.7; chapter 11
Problems: 10.7.4, 11.3.3, 11.4.6

Lecture 17         2:30 - 4:00 tuesday, May 25, 1999 in Tech M120
Strange attractors
Reading: chapter 12

Lecture 18         2:30 - 4:00 thursday, May 27, 1999 in Tech M120
Chaotic averaging: escape rates

Reading period starts

Lecture 19         2:30 - 4:00 tuesday, June 1, 1999 in Tech M120
Chaotic averaging: escape rates?
Problems: we concentrate on the term paper projects

Lecture 20 (the last of the course)     2:30 - 4:00 thursday, June 3, 1999 in Tech M120
What's wrong with this course?
A moment of truth; exhaustion has sat in, so we cancelled the lecture.

morning of Friday, June 4:

Download the final exam in either pdf (447 Kb) or postscript (1.8 Mb) format .
The exam involves analysis of a dynamical system (fixed points, stability, bifurcations) and numerical experimentation with integration of a set of differential equations describing the system.

If you are working on your own project, but have discovered that it is too ambitious for this course (it is enough to work through somebody's good published paper, one does not need to produce a piece of frontline research), and you are not satisfied with your progress, this is the last day to give up on the project, and take the exam instead.

Reading: the whole course

Alernative:
Term papers

         due before 4:00 PM tuesday, June 8, 1999 - Predrag's office, Tech F332


Predrag Cvitanovic', p-cvitanovic@nwu.edu