Lab 2 - Intro. to Nonlinear ODEs
Lab 3 - Subspaces and Manifolds
Lab 6.5 - To the Hopf Bifurcation
Lab 7 - Excitable Systems and the Hopf Bifurcation
Lab 10 - Scalar Maps with Parameters
Lab 12 - Delay Differential Equations (Logistic Equation)
Examples will come primarily from biology as predator-prey
interactions, cell membrane electrophysiology and networks
of excitable cells, cell regulatory networks, population
models, among other examples. We will discuss ODE systems
which come from discretization of spatial operators and
from the wave approximation.
Lectures/Tutorials will be given on Tuesdays and the assignments may
be completed on Thursdays or outside of the lab.
Texts:
Class: 4:00-5:00p.m. TTh,
Symonds I (2nd floor Fondren)
Office: DH 3023
Email: bpeercy@caam.rice.edu
Phone: 713-348-6113 (office)
Office hours: Th 10-12 and by appointment
Class web page:
http://www.caam.rice.edu/~bpeercy/math468/syllabus.html
Motivation: The point of the dynamical systems lab is to enhance the
theory seen in the lecture portion of the course with
concrete, hands-on examples of ordinary differential
equations (ODEs). In doing so, we will examine several
types of physical systems which lend themselves to
modeling by ODEs. We will likely concentrate on
low-dimensional models as to be able to visualize their
dynamics in a phase plane (Matlab's pplane5), however, we
will use the power of Matlab to compute and visualize
aspects of higher dimensional systems, as well.
Lab Evaluation: You will be given a weekly lecture/tutorial and
assignment due the following week. These will
comprise the lab portion of your course grade. For
graduate students the write-up of assignments should
be done using the appropriate word processor
(i.e. LaTeX, etc.) to be used for thesis writing. The
write-up should include an appropriate amount of
english to convey to the reader the set-up, relevance
of included figures, and a conclusion.
Differential equations and dynamical systems,
Perko, 2001
Dynamics and Bifurcations,
Hale and Kocak, 1991
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector
Fields,
Guckenheimer and Holmes, 1983
Computational Biology,
Fall, Marland, Wagner, and Tyson, 2002
Mathematical Physiology,
Keener and Sneyd, 1998