Syllabus

Class: Physics 4267/6268, Nonlinear Dynamics & Chaos, Fall 2012

Instructor & TA

Instructor:

Prof. Daniel I. Goldman, School of Physics, Georgia Institute of Technology
Office: Howey C202 (office hours: by email)
Phone: (404) 894-0993
E-mail: daniel.goldman@physics.gatech.edu

TA:

Ellen Liu
Office: Howey (office hours TBD)
E-mail: eliu82@gatech.edu

Course Description

The course offers an introductory treatment of nonlinear dynamics and chaos, including first order ODE and their bifurcations, phase plane analysis, limit cycles, Lorenz equations, chaos, iterated maps, period doubling, fractals and strange attractors. Teams of students will also conduct one week of self-guided experiments in Prof. Goldman's laboratory and prepare final report/presentation of the results.

Time and Place

Tuesday, Thursday, 2-3:15PM

Class: Howey L5 Lab: W203

Homework and Grading

Homework assignments will be posted on the web every Monday and will be due next Monday. You can discuss problems with each other, but the solutions have to be executed and submitted individually. In general you are expected to comply with the academic honor code. There will also be one midterm exam and a final. The overall grade for the course will be based on the homeworks (~10%), mid-term exam (~20%), final exam (~20%) and a final project (~50%).

Books

"Nonlinear Dyanamics & Chaos", Steven H. Strogatz (Westview Press, 2001)

"Pattern Formation and Dynamics in Nonequilibrium Systems", Cross & Greenside

Course Topics

Geometrical analysis of ODEs and bifurcations

Maps

Fractals

Pattern formation

Hands-on experiment/simulation/theory via virtual "microlabs"

Important dates

Midterm exam (take home): March 13, due March 17

Final project talks: April 19,24

Final exam due (report and problems): May 2

Course Outline & Schedule

Jan 9: Lecture 1, intro to the subject

Jan 11: Lecture 2, intro to 1D systems, geometric methods to solve ODEs (Chap 2)

Jan 18: Lecture 2, continued from before, class project discussion (Chap 2)

Jan 23: Lecture 3, Linear stability analysis, existence and uniqueness, finite time singularities (Chap 2)

Jan 25: Lecture 4, numerical methods for solving ODEs (Chap 2)

Jan 30: Lecture 5, intro to bifurcations, (Chap 3)

Feb 1: Lecture 6, imperfect bifurcations (Chap 3)

Feb 6: Lecture 7, flows on the circle/entrainment (Chap 4)

Feb 8: Lecture 8, 2D systems (linear) (Chap 5)

Feb 13: Lecture 9, Nonlinear 2D systems (Chap 6)

Feb 15: Lecture 10, Conservative nonlinear 2D systems (Chap 6)

Feb 20: Lecture 11, Limit cycles (Chap 7)

Feb 22: Lecture 12, Relaxation and weakly nonlinear oscillators, perturbation theory (Chap 7)

Feb 27: Lecture 13, Bifurcations in 2D (Chap 8)

Mar 1: Lecture 14, Quasiperiodicity, Poincare maps, Floquet theory (Chap 8)