Lecture: Tuesdays and Thursdays, 2:30 - 3:45, 833 Eigenmann
Instructor: Randall D. Beer
Office: 840 Eigenmann
Phone: 856-0873
Email: rdbeer [AT] indiana [DOT] edu

Course Description
Concepts from dynamical systems theory are becoming increasingly important in cognitive science, and the construction and evaluation of dynamical models requires a thorough understanding of the mathematical theory of dynamical systems in the same way that computational models in cognitive science require a thorough understanding of computation. This course provides such an introduction to dynamical systems theory, with an emphasis on the underlying mathematical ideas and tools. Although we will focus on dynamical systems formed by sets of differential equations, we will also cover discrete-time dynamical systems at several key points. The course will begin with a comprehensive study of one and two-dimensional systems and then proceed to the general case. At each step, we will examine the limit sets, stabilities, phase portraits and bifurcations that are characteristic of that dimension. Throughout the course, applications drawn from a wide variety of areas will be used to illustrate the mathematics. We will also make heavy use of computer tools for analysis and visualization.

Text
Nonlinear Dynamics and Chaos by Steven H. Strogatz

Software
All in-class examples will make use of Mathematica, which is available to students for $25 through the Stat/Math Center. However, if you wish, you may choose to do your homework assignments in another comparable software package, such as Matlab or Maple.

The Mathematica package Dynamica will also be used in class and may be used by students on assignments except where explicitly disallowed. If you will not be using Mathematica for your assignments, other available dynamical systems software is listed at the bottom of this page.

Grading

Assignments	50%
Midterm	25%
Final Exam	25%

Although students are encouraged to discuss course material outside of class, all work that you turn in should be your own.

Assignments

• None yet

Topics

• Introductory Material
• Course Overview
• A Gentle Introduction to Dynamical Systems Theory
• 1-Dimensional Dynamics
• Dynamics on a Line
• Bifurcations on a Line
• Dynamics and Bifurcations on a Circle
• A Taste of Bifurcation Theory
• 2-Dimensional Dynamics
• Equilibrium Points in the Plane
• Limit Cycles in the Plane
• Bifurcations in the Plane
• An Extended Example: The Fitzhugh-Nagumo Model
• Dynamics and Bifurcations on a Torus
• n-Dimensional Dynamics
• Dynamics in Euclidean Space
• Chaotic Dynamics
• Bifurcations in Euclidean Space
• Additional Topics
• Nonautonomous Dynamics
• Infinite-Dimensional Dynamics
• Hybrid Dynamics
• Course Summary

Supplementary Material

• None Yet

Resources

• Dynamical Systems Software
• Dynamica
• MatCont
• XPPAUT
• AUTO
• Complete List
• Dynamical Systems
• ChaosWeb
• Dynamical Systems Magazine
• Encyclopedia of Dynamical Systems
• Mathematica
• Wolfram Research
• Mathematica Tutorials
• Getting Started with Mathematica at IUB