Introduction to Nonlinear Dynamics and Chaos
AMATH 402/502
WINTER 2014
Instructor  TAs 

Professor Joel Zylberberg 

326 Lewis 

Office hours: Wed and Thurs 34 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 4:005:00 (skype: amath402502ta ) Mauricio: Th 10:3011:30 (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
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
FOR THE 502 CLASS ONLY HW6: Due Friday Feb 21
FOR THE 402 CLASS ONLY HW6: Due Friday Feb 28
The Lorenz 1963 paper associated with HW8
Homework Solutions:
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 solutions.
Winter 2010 midterm exam (no solutions provided)
Winter 2013 final exam (no solutions provided)
Winter 2006 Final exam Solutions
TOPICS:
(1) Onedimensional systems
Firstorder ordinary differential equations and initialvalue 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) Discretetime 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 oncampus 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.