Mathematical Biology 3380: Pattern Formation

Monday/Wednesday 9:30-10:45

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.

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