Introduction to Nonlinear Dynamics and Chaos
AMATH 402/502

 

WINTER 2012

Instructor	TAs
Professor Eric Shea-Brown	Ben Lansdell Susie Sargsyan
Office hours -- in Guggenheim 415F	Office hours -- in Guggenheim 406
W 4-5 PM (starting Jan 11) via skype during office hours: ericsheabrown please call my office 206 685 6635 during office hours if I've forgotten to turn on skype	M: 4:00-5:00 Tu: 10-10:30 EDGE/SKYPE ONLY Tu: 10:30-11:30 Th: 10:00-11:30 via skype during office hours: ben.lansdell

Scheduling

HW due most Fridays at 12:30 PM -- in labeled box near elevator, 4th floor Guggenheim Hall.

MT: Friday Feb. 10, in class

FINAL: Please see time schedule

 

*** LINK TO COURSE MOODLE PAGE ***

or type

moodle.extn.washington.edu

into browser ...

 

Textbooks, Notes, and Course Resources

The required text for this course is Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, by S. Strogatz. Perseus Books, 2001.

Also: Prof. Bernard Deconinck's course notes for AMATH 402/502 -- linked through moodle page above.

OTHER COURSE RESOURCES:

Opinion/review piece on catastrophe theory -- Nature 1977

Video by S. Strogatz -- Nonlinear dynamics and chaos: Lab demonstrations

JAVA and MATLAB software for odes -- pplane and dfield

 

TOPICS:

(1) One-dimensional systems
First-order ordinary differential equations and initial-value problems
Nonlinear differential equations and flows on the line
Bifurcations
Flows on the circle

(2) Two (and higher)-dimensional flows
Linear equations with constant coefficients: matrices and eigenvalues
The phase plane
Limit cycles
Bifurcations in two dimensional systems

(3) Discrete-time systems
Introduction to maps

(4) Chaos
Logistic map.
The Lorenz equations
Additional topics in fractals and chaos

CODE: logistic_map_demo.m, sin_map_demo, logistic_map_simulate_in_time.m, lorenz_sim_and_traj , henon_simulate_in_time

MOVIE: synchronized fireflies!

 

EXAMS AND GRADING:

Midterm

closed book, 1-sided notebook-size sheet of notes, no calculators

!!!! BRING A BLANK EXAM BOOK TO THE MIDTERM !!!!

*** Edge students: contact EDGE office for exam arrangements -- as per their instructions, exams are done remotely in most cases. ***

Final

closed book, 2-sided notebook-size sheet of notes, no calculators

!!!! BRING 2 BLANK EXAM BOOKS TO THE FINAL !!!!

Edge students: contact EDGE office for exam arrangements.

Homework

Late HW is not accepted, but the lowest HW score will be dropped. This policy is meant to assist in unexpected situations. In unusual extenuating circumstances involving more than one week, please contact the professor.

Homework is graded statistically.

Your course grade will be calculated via the following weights: homework 25%, midterm 30%, final 45%.