Interdisciplinary Nonlinear Dynamics

ESAM 438 Fall 2000

Hermann Riecke

This class gives an introduction to nonlinear dynamical systems as they arise in a wide range of areas of science and engineering. While the main goal of the class is to present the concepts and techniques needed for dealing with these systems it will do so from an applied perspective making contact with physical systems wherever possible. The course will follow the textbook Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering by S. Strogatz.

The Fall Quarter course will be followed by a projects-based course in Spring Quarter on ?????????????, which will be directed by M. Johnson (BME, 467-7143) and S. Lichter (ME, 467-1885).

Figure 1: a) Period-doubling cascade and chaos in logistic map. b) Snapshot of spiral-defect chaos in fluid convection (courtesy E. Bodenschatz).

Key topics to be discussed include

• Phase space representation of dynamical systems, flows, fixed points, orbits.

• Bifurcations: qualitative change in behavior.

• Nonlinear oscillators

• Weakly nonlinear theory, center manifold reduction, multiple scales.

• Pattern formation

• Chaos, Lorenz system, strange attractors, logistic map, renormalization.

Location and Time: TuTh 10:30-12:00 TCH M152

For more information call, send e-mail, or stop by: 491-8316; h-riecke@nwu.edu; M458.

This course is part of the new IGERT program Complex Systems in Science and Engineering

                       http://www.esam.nwu.edu/IGERT