Nonlinear Dynamics and Chaos - A Toolbox for Complex Systems Research

Alfred W. Hubler

This course provides a broad introduction to the nonlinear dynamics of physical systems with varying degrees of complexity. We will survey a variety of concepts associated with (but not limited to) bifurcation phenomena, mappings & difference equations, strange attractors, nonlinear oscillations, chaotic behavior, adaptive systems & adaption to the edge of chaos, control of chaos, symbolic sequences, biomechanics and singular motion, entrainment, dissipative systems, nonlinear signal processing, catastrophes, adaptive computation, evolutionary dynamics, traffic jams, Markov processes, Brownian motors & rachets, and universal scaling.

The main theoretical concepts are:

• genetic algorithms  • fractals & fractal growth
• cellular automata• percolation
• nonlinear dynamics• solitons, multi-solitons, swarms
• agent-based modeling• neural networks
We will investigate models of dynamical systems drawn from physics, engineering, chemistry, biology, economics, finance, and sociology.

In addition students receive a hands-on introduction in programming MatLab, Mathematica, and some more advanced programming languages.

There is a homework assignment at most lectures.

The course grade is detetermined from homework (40%), three hour exams (10% each), and a final exam (30%). There is up to 10% extra credit for extra credit homework problems. There is up to 20% extra credit for a semester project. The semester project includes weekly meetings and a term paper. Topics for the semester project are listed here.

Visitors please use screenname guest with password cp2000.

Office Hour Tu 11am-noon, 4-125 ESB, 217-244-5892 (w) 217-328-7701 (h)

Lecture Notes
Homework Overview
Equation Sheet
Recommended Books

Exam Dates

This courseware was created with support from NSF grant 0140179.
Background reading on the future of university research: NY Times article