Nonlinear Dynamics and Chaos
This is a doctoral course that follows Steve Strogatz’s excellent book “Nonlinear Dynamics and Chaos”
Image credit: from www.stevenstrogatz.com
PhD course Nonlinear Dynamics and Chaos (Course coordinator)
Nonlinear dynamics is an area of mathematics with a wealth of applications to biology and physics. This course delves into the behavior of nonlinear systems, which often exhibit unpredictable and complex behavior. Unlike linear systems, whose outputs are directly proportional to their inputs, nonlinear systems can demonstrate a wide variety of phenomena, including sensitivity to initial conditions, bifurcations, and strange attractors. This course will explore the mathematical underpinnings of these phenomena, using both analytical and computational techniques. The purpose of this course is to provide an introduction to the topic as we work through a well-known textbook (a classic) on the subject. By the end of this course, students should be equipped to analyze and predict the behavior of nonlinear systems. Below are a sample of the topics the course covers.
- flows on lines and circles
- stability and bifurcation analyses
- limit cycles
- fractals
- oscillators
- chaos and strange attractors
We also study many fun problems with enticing names including: “rabbits vs sheep”, “love affairs”, and “fireflies”.
The primary text is Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistry, and Engineering by Steven Strogatz (ISBN 9780367026509). Additional material is drawn from the excellent nonlinear dynamics course offerings on Complexity Explorer led by Liz Bradley.
Last offered: Fall 2024
