Introduction to Nonlinear Dynamics and Chaos
AMATH 402/502

 

WINTER 2014

Instructor TAs
Professor Joel Zylberberg

Kameron Harris

Mauricio Del Razo Sarmina

326 Lewis

Office hours: Wed and Thurs 3-4 pm

I will be on Skype during my office hours for EDGE students and anyone else who can't make it in person

Skype name: joelzy.amath

Office hours: 129 Lewis

Kam: Tue 4:00-5:00 (skype: amath402502ta )

Mauricio: Th 10:30-11:30 (skype: amath402502ta )

Scheduling

HW due most Fridays at 3 PM

MT: In class on Feb 19 for AMATH 402

MT: In class on Feb 26 for AMATH 502

Final Exam (for AMATH 402): March 20. See UW Exam schedule to confirm this

Final Project (for AMATH 502): Due by 3pm, Friday March 14 (Info available here)

 

Online discussion forum

*** LINK TO COURSE PIAZZA PAGE (you will need to log in) ***

or type

https://piazza.com/washington/winter2014/amath402502/home

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

And…: A list of topics that the instructor finds particularly important. You can and should use this as a study guide!

Online Video Lectures: Videos of the (502) lectures will be available here (UWlogin required)

Supplemental readings

For interest, here is A great recent paper on limit cycles and bifurcations in biological oscillators.

Here is the 1990 Lengyel et al. paper on the oscillating reaction we discussed in class

Here is the 1967 Mandelbrot paper "How long is the coast of Britain" on fractals

Here is the famous "Period 3 implies chaos" paper by Li and Yorke.

OTHER COURSE RESOURCES:

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

JAVA and MATLAB software for odes -- pplane and dfield

 

Homework Assignments:

EDGE STUDENTS PLEASE UPLOAD YOUR WORK TO CANVAS

Midterm Exam and Solutions:

AMATH 402 Midterm exam questions and solutions / rubric

AMATH 502 Midterm exam questions and solutions / rubric

Sample Exams:

Winter 2013 midterm exam. NOTE: this exam is a bit too long. Don't stress if it takes you 1.5 hours to do.

Winter 2013 midterm exam solutions.

Winter 2010 midterm exam (no solutions provided)

Winter 2013 final exam (no solutions provided)

Winter 2006 Final exam

Winter 2006 Final exam Solutions

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 in class

!!!! 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. ***

Students in virtual sections: will take exam in class at same time as other on-campus students.

Final Exam (402 only!)

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

Homework due most Fridays.

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:

AMATH 402 : homework 30%, midterm 30%, final exam 40%

AMATH 502 : homework 30%, midterm 30%, final project 40%

 

U Washington takes academic honesty very seriously! You are expected to uphold the strong academic tradition here at UW.