(consult http://www.phy.duke.edu/Courses/213 for updates)

Instructor:

Bob Behringer

(Physics Rm. 095, 660-2550, bob{at}phy.duke.edu)

(Rm. 0065 Physics, xg6{at}phy.duke.edu)Grader:

Sam Gong

Class time:Tuesday/Thursday 8:30 PM - 9:45 PMOffice Hours:M 4:00 - 5:00 PM (BB)

[ Problem Assignments ]

Introduction

This course is a graduate-level introduction to nonlinear dynamics: we examine linear and and nonlinear instabilities in mathematical, physical, chemical and biological systems that evolve in time. It is also appropriate for upper division undergraduates, including physics majors, and other students with preparation in introductory physics and in solving differential equations (ordinary and partial).

Grades:Grades will be assigned according to the following weighted average:

- Problem Sets (assigned every one to two weeks): 30%
- Midterm exam and Final exam: 20% each
- Final Project: 30%

Prerequisites

- Exposure to the mathematics covered in MTH 111.
- Exposure to the physics covered in PHY 51 and 52.
- SOME experience with a programming language like Basic, FORTRAN, or C.

Topics

Overview of Chaos and Dynamical systemsOne-dimensional flowsBifurcationsTwo-dimensional flowsOne-dimensional mapsStrange attractors and fractal dimensionsDynamical properties of chaotic systemsPhase space, manifolds, Lyaponov exponents, time series analysis, controlSpecial topicsApplications

Academic Integrity

Homework Assignments:Collaborating on the problem sets by discussing approaches is OK, but please remember that you learn from these mostly by struggling through them for yourself. Do not let others solve them for you. Also, it pays to start early.

Exam Policy:No collaboration on exams is allowed. No books, notes or calculators are allowed.