Introduction to Nonlinear Dynamics and Chaos
AMATH 402/502

 

WINTER 2013

Instructor	TAs
Professor Joel Zylberberg	Pedro Maia Kameron Harris
326 Lewis
Office hours: Tuesday and Friday 3:30-4:30 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 Kam: W 11:00-12:00 (skype: kamerondeckerharris) Pedro: Th 10:30-11:30 (skype: theamath581ta Yes it says 581, and Pedro is TA'ing 402/502)

Scheduling

HW due most Fridays at 3 PM

MT: Feb 13 in class

 

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

or type

https://piazza.com/class#winter2013/amath40250

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 (running) list of topics that the instructor finds particularly important. You can and should use this as a study guide!

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

OTHER COURSE RESOURCES:

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 in class, Wed Feb 13

!!!! 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

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

Edge students: contact EDGE office for exam arrangements. Students in virtual sections: will take exam at same time as other on-campus students.

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 40%.

 

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