Mathematical Biology 3380: Pattern Formation
Spring 2019
Monday/Wednesday 9:30-10:45
Benedum G28
Bard Ermentrout
Office Hours: Mon 3:00-4:00, Wed 11-12:00 and most other times by appt
Recommended reading
Pattern Formation: An Introduction to Methods
Rebecca Hoyle (this will be the official text of the course, but I will use a lot of my notes)
Cross and Hohenberg
Mathematical Biology II
J.D. Murray, Springer, 2004
Anything on Phil Maini's publ list !
Prerequisites
Mathematics
Some differential equations
Some basic linear algebra (eigenvalues, etc)
Some Fourier series
Computing. You will be required to do some computer exercises. Free software
XPPAUT
is available that will allow you to do most of the exercises. However, if you are more comfortable with MatLab, or other software, by all means use it.
Grading
Homework 60%
Final Project 40%
Syllabus
Overview and introduction
Lecture 1
Here is my result from the oil experiment
Lecture 2
Lecture 3
Should take about 2 wks
Lecture 4
Group stuff snd calcs
Lecture 5
Hexagons and waves
Lecture 6
Targets, spirals, chemotaxis
Discrete models
Competition
Ring geometry
Eigenspace decomposition
Applications
Pulse coupled oscillators
Cellular systems
PCA
HOMEWORK 1
Due Jan 23.
Linear theory of Reaction-diffusion and other equations
HOMEWORK 2
Due Feb 12
Nonlinear analysis of pattern formation
Liapunov-Schmidt reduction
Symmetry methods
Applications to planar problems with different lattices
HOMEWORK 3
Due Feb 26.
Some nice Java applets to explore pattern formation
Brusselator applet
HOMEWORK 4
Due Mar 27
PDE models
Long wave approximations
Kuramoto-Shovashinsky equations
planar bifurcations
Ginzberg-Landau
Some XPP files for 1-d CGL
Swift-Hohenberg equations
HW 5 - at long last!
Due at the end of classes
Cellular automata
Waves
Spatiotemporal chaos