Introduction to Nonlinear Dynamics and Chaos
AMATH 402/502
WINTER 2015
Instructor  TAs 

Professor Joel Zylberberg 

326 Lewis 

Office hours: Mon and Tues 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 Yian: Wed 2:303:30 (skype: amath402502ta ) Yue: Thurs 4:005:00 pm (skype: amath402502ta ) 
Scheduling
HW due most Fridays at 4 PM (Schedule, and homework scores, available via UW Canvas)
MT: In class on Wed Feb 11 2015
Final Exam (date TBA). See UW Exam schedule for details
Online discussion forum
We'll use the Piazza system for online discussion of questions arising from lectures, or homework, etc. Please post and answer questions there. The TA's and Professor will also answer questions posted there.*** LINK TO COURSE PIAZZA PAGE (you will need to log in) ***
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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 2015 (502) lectures will be available here (UWlogin required)
For reference, videos of last year's (2014) lectures are available here (UWlogin required)
Supplemental readings
Here is the Hopfield 1982 paper using Lyapunov functions to understand the dynamics of associative memory systems.
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.
John Guckenheimer's famous work on geometric Lorenz attractor "Structural stability of lorenz attractors"
Yian Ma's work, which further simplified the attractor to be the Baker map on the Ponicare section "Potential Function in a Continuous Dissipative Chaotic System: Decomposition Scheme and Role of Strange Attractor"
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
The Lorenz 1963 paper associated with HW8
Homework Solutions:
Sample Exams:
Winter 2013 midterm exam solutions.
Winter 2010 midterm exam (no solutions provided)
AMATH 402 Wi2014 Midterm exam questions and solutions / rubric
AMATH 502 Wi2014 Midterm exam questions and solutions / rubric
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
Code from David Goodmanson for making bifurcation diagrams  and examples of its useMOVIE: 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
!!!! 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:
homework 30%, midterm 30%, final exam 40%
U Washington takes academic honesty very seriously! You are expected to uphold the strong academic tradition here at UW.