Nonlinear Dynamics I: Chaos
Joint Subject Offering: 12.006J/18.353J/2.050J
Instructors: Daniel H. Rothman and Thomas Peacock
Introduction to nonlinear dynamics and chaos in dissipative systems. Forced and parametric oscillators. Phase space. Periodic, quasiperiodic, and aperiodic flows. Sensitivity to initial conditions and strange attractors. Lorenz attractor. Period doubling, intermittency, and quasiperiodicity. Scaling and universality. Analysis of experimental data: Fourier transforms, Poincaré sections, fractal dimension, and Lyaponov exponents. Applications to mechanical systems, fluid dynamics, physics, geophysics, and chemistry. See 12.207J/18.354J for Nonlinear Dynamics II.
This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.
The course concentrates on simple models of dynamical systems, their relevance to natural phenomena, and methods of data analysis and interpretation. The emphasis is on nonlinear phenomena that may be described by a few variables that evolve with time. The theory of nonlinear continuum systems is covered in the sequel to this course, 12.207J/18.354J.
To promote the notion of numerical experiments, we assign several laboratory-like problem sets that require the use of a computer (e.g., an Athena workstation). The computer exercises will usually use Matlab, but students are free to use whatever software tools and computers they desire. No previous experience with numerical computation is necessary.
This is an undergraduate course. Graduate students are reminded that this course carries no graduate credit and are encouraged to take 18.385 instead.
Prerequisites: 8.02, 18.03. Knowledge of ordinary differential equations is essential. Some linear algebra (knowledge of eigenvectors and eigenvalues) is also necessary. Having some experience with numerical computation is helpful but not necessary.
Lectures: Tuesdays and Thursdays from 11:00-12:30 in room 66-168.
© Dan Rothman Group, 1999-2005
last updated: Wed Sep 5 12:58:45 2007