Introduction to Nonlinear Dynamics and Chaos
AMATH 402/502



Instructor TAs
Professor Joel Zylberberg

Yian Ma

Yue Wang

326 Lewis

Office hours: Mon and Tues 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

Yian: Wed 2:30-3:30 (skype: amath402502ta )

Yue: Thurs 4:00-5:00 pm (skype: amath402502ta )


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 on-line 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.

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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

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 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"


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

JAVA and MATLAB software for odes -- pplane and dfield


Homework Assignments:


HW1: Due Friday Jan 16

HW2: Due Friday Jan 23

HW3: Due Friday Jan 30

HW4: Due Friday Feb 6

HW5: Due Friday Feb 20

HW6: Due Friday Feb 27

HW7: Due Friday March 6

HW8: Due Friday March 13

The Lorenz 1963 paper associated with HW8

Homework Solutions:

Solutions to HW1

Solution HW2

Solution HW3

Solution HW4

Solution HW5

Solution HW6

Solution HW7

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)

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

Winter 2006 Final exam Solutions


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

Code from David Goodmanson for making bifurcation diagrams -- and examples of its use

MOVIE: synchronized fireflies!



Midterm in class


*** 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


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.