MCE567: Experimental Nonlinear Dynamics

Exploration of Practical Aspects of Dynamical Systems Theory

Catalog Description:
Fundamentals of the experimental analysis of nonlinear dynamical systems; mathematical concepts and algorithmic tools to characterize, analyze, model and predict dynamics of nonlinear systems. (Lec. 3). Prerequisite: MCE 366 or MCE 464 or equivalent. Class Number for Spring 2008: 7078.

Required Text:
Holger Kantz and Thomas Schreober, Nonlinear Time Series Analysis, Second Edition, Cambridge University Press.

Suggested Optional Texts:
(1) Julien C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, 2003,
(2) Lawrence N. Virgin, Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration, Cambridge University Press, Cambridge, UK, 2000, and
(3) Chaos in Ecology: Experimental Nonlinear Dynamics, Academic Press, Elsevier Science, 2003.

Course Description

Meeting Place and Time: Wales Hall 226 on Tuesdays and Thursdays from 8:00AM -- 9:15AM.

Nonlinear dynamical systems play important role in every field of science and engineering. This subject, in contrast with linear dynamical systems, is still emerging and many of its original methods and tools are not widely known. This course is aimed at providing fundamentals of the experimental analysis of nonlinear dynamical systems. It will focus on main mathematical concepts and algorithmic tools that characterize, analyze, model and predict dynamics of nonlinear systems.

The course will begin with a discussion of the nature and origins of nonlinear systems in nature and engineering. All the discussions will be framed in the general dynamical systems perspective. The fundamental concepts of the statistical and spectral analysis of linear systems will be reviewed from this perspective to provide a basis for the discussion of nonlinear systems. Important experimental considerations such as sampling theory, resolution, aliasing, filtering, etc. will also be reviewed. Main course will cover dimension theory; estimation of fractal dimensions; delay coordinate reconstruction and ``embedology;'' stability, local and global bifurcations, and Lyapunov exponents; invariant manifolds, attractors and their dimensions; nonlinear modeling and forecasting. Use of experimental analysis in modeling of nonlinear systems will be discussed throughout the course using practical examples of variety of natural and engineering systems.

News and Announcements 04/12/2008: Finally, the Matlab program scripts for average mutual information, kd-tree partitioning for nearest neighbor serch, false nearest neighbors, correlation dimension, and Lyapunov exponent are posted on the hanout page.

03/10/2008: Solution to the third assignment. Also the solution to the second assignment.

02/26/2008: Assignment 3 and corresponding m-files: (1) Duffing equation equilibrum points and corresponding bifurcations: demo.m, and (2) forced damped two-well Duffing equation: twowell.m.

02/19/2008: Assignment 2: Exercises 2.1 and 2.2 from the textbook. Due: 02/26/2008.

02/18/2008: Handouts for Aliasing and Windowing are posted.

02/14/2008: Solution to the first assignment.

02/12/2008: Notes on Power Spectral Density.

02/05/2008: First assignment.

12/17/2007: Interested students should register now so that course is not cancelled.

12/15/2007: course add posted.

Interesting Materials :03/11/2008: Here's an illustrative applet that shows Peano Construction that I have mentioned in the class.

Open Software packages listed on iMechanica.

Oh, By The Way - Pink Floyd

Professor Chelidze's Course Web Pages