Chaos and Complexity Courses for Fall 2001, UW-Madison


Mathematics 415

Applied Dynamical Systems, Chaos and Modeling

An upper level undergraduate course that introduces students to the study of nonlinear dynamical systems. The course will be taught from an applied mathematics standpoint, with emphasis given to the applications of the theory.

Course Description

1. One-dimensional maps and difference equations: linear and nonlinear problems, graphical solutions, bifurcations, chaos.

2. First--order differential equations (one--dimensional flows): linear and nonlinear equations, graphical solution, bifurcations.

3. Two--dimensional flows: phase plane, stability of fixed points, periodic solutions and limit cycles; Introduction to bifurcation theory, local and global bifurcations, Tools for studying global behavior of flows: Lyapunov functions, Poincare--Bendixson Theorem, gradient flows.

4. Three--dimensional flows: Lyapunov exponents, Poincare sections, strange attractors, chaos.

5. Each of the topics will be discussed with references to applications in Mechanics, Population Dynamics, Biological Oscillators, Neurophysiological Models, Chemical Oscillators, and others. Computers will be used for mathematical experimentation and to aid in visualising solutions.

Instructor: R. Turner, 262-6272,

Time and Place: Monday, Wednesday, Friday, 9:55. Van Vleck B235

Call Number: 28188

Text: Strogatz, S. H., Nonlinear Dynamics and Chaos

Prerequisites: Math 319, or Math 320, or consent of instructor.

NOTE: Although the course is taught at the 400 level, some graduate students from engineering, the physical sciences and mathematics might benefit from the course.

Mathematics Of Biological Computation and Bioinformatics
Instructor: Amir Assadi (Fall 2001)

This course introduces selected topics from mathematical and computational methods that are currently used for research in molecular biology and bioinformatics focusing on: pattern recognition and analysis of massive data sets, modeling computation and information processing in biological systems. These include: computational methods in learning theory and intelligent systems (e.g. associative memory, back propagation and Hopfield networks), complex dynamical systems. There will be a hands-on computation/mathematics lab hour that covers tools such as Fourier and wavelet methods for processing signals and images; statistical and probabilistic methods such as PCA, ICA and Hidden Markov Models. Discussions are in a lecture/lab environment with hands-on computation exercises. Several hands-on computer lab tutorials will be provided to help with the computational background in design of algorithms (e.g. Optimization, Neural Networks, Genetic Algorithms, Evolutionary Programming...) Much of the mathematical and computational techniques are equally useful in Genomics, Proteomics, and cellular biology. The grade for the course will be based on a term project. Mathematics and engineering/science students are not required to know molecular biology, but to learn the relevant topics simultaneously through reading or other courses.

Course No. Math 991. Monday and Wednesday 3:30-4:45
(Lecture and Computation Lab).

Prerequisites: Consent of Instructor for undergraduate students. Mathematics: linear algebra, calculus, and preferably basic statistics/probability. Biology: Students without biology background will be asked to read some background materials (that will be distributed as needed) in addition to the lecture materials. Please consult with URL for more information and sample projects.

Textbooks (Recommended Only)

  1. Gustavo Deco and Bernd Schuermann: Information Dynamics;
  2. HF Nijhout, Lynn Nadel, and Daniel Stein: Pattern Formation in the Physical and Biological Sciences;
  3. Klaus Mainzer: Thinking in Complexity.

The advanced interdisciplinary course 777 Nonlinear dynamics, bifurcations and chaos is offered this Fall.

For details see

(If you would like to display a poster for 777, you can download it from this web site)

Ian Dobson,
ECE Department

Chaos and Complex Systems Seminar Page