Welcome to ME 961
Nonlinear Dynamics and Chaos
Introduction:
The world is full of nonlinear phenomena. Rattling in machines, squealing of brakes, turbulence, flow-induced vibration, motion of ships, chattering of machine tools, phase transformation in materials, synchronization of fireflies, fibrulation of the heart, the firing of neurons, congestion of traffic, the snoring of noses...the list goes on and on. Nonlinearity can give rise to behavior not found in linear systems.
In this course will be devoted to the analysis of nonlinear models. We will look at models in the form of ordinary differential equations and iterated maps. It is often not possible to come up with quantitatively accurate analytical solutions. The goal will be to understand the qualitative nature of the responses. In this way we can predict the trends in how the dynamics depends on parameters.
Some of the things we will do: review of linear stability, center manifolds and normal forms, averaging, local bifurcations of equilibria, bifurcations of periodic dynamics, chaos and symbol dynamics.
Instructor:
Brian Feeny
2328C Engineering Building
feeny@me.msu.edu
3-9451, 3-1750 (fax)
Time: M, W, F 4:10-5:00, 1225 EB
Credits: 3
Topics: outline
Text: Most of the course is based on "Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields," by Guckenheimer and Holmes. Other references will be posted.
Grading: based on homework and exams, to be determined.
Prerequisite: vibrations, controls, linear systems, or ODEs.
Newsworthy Nonlinear Dynamics