PIMS IGTC - Mathematical Cell Biology Summer Course UBC 2012

Notes By: William Holmes

Main Course Website

Topics

-Local Perturbation Analysis - Bifurcation analysis of Reaction Diffusion Equations

-Bifurcation analysis using Matcont

-Wave pinning and Actin Waves - Models and analysis.

Materials

Slides

Lecture 1: LPA - Theory and Context

Lecture 2 : LPA - Finer Points

Lecture 3 : Matcont for Bifurcation Analysis (With associated matcont examples)

Lecture 4 : Wave Pinning, Actin Waves, and LPA (With associated matcont examples)

Recorded Videos

The following are pre-recorded videos pertaining to various topics discussed in these notes. The quicktime videos are relatively large (~25 Mb) but are better resolution than the youtube versions.

Matcont Intro: Youtube: Quicktime : Introduction to Matcont

Pitchfork 1: Youtube: Quicktime : Practical example of matcont. Using matcont to compute an equilibria and continue with respect to an equilibrium for the pitchfork system.

Pitchfork 2: Youtube: Quicktime : Extension of Pitchfork 1. Extracting a branch point from an equilibrium curve, branch switching, and continuation along an extra branch through a branch point.

Matlab Codes / Matcont Materials

The following are codes associated with the examples discussed in these notes and videos. In each case, two matlab files are provided. One includes the matlab function file used to encode information about the system in 'Matcont' format. These are compiled by matcton from the information typed in the GUI. A command line driver is also included. All examples performed using the GUI can also be performed from the command line (eg. integration, equilibrium continuation). The driver files show examples of how to do this. The benefit of this approach is it is higher throughput and makes passing data to plotting scrips simpler.

One note about using this software package. It can be a bit tricky for Mac OSX - Lion users. Matcont (and many other matlab packages) need access to a C-compiler to some background files. OSX - Lion no longer comes with built in compilers. So you will need to add them before you can use this program. This is relatively easy and does not require much tech savy. Here are some instructions for how to install a C-compiler and link it to matlab.

Pitchfork Codes: Matcont Function : Command Line Driver - Fully Documented

Schnakenberg Codes: Matcont Function : Command Line Driver

Wave Pinning Codes: Matcont Function : Command Line Driver

Actin Wave Codes: Matcont Function : Command Line Driver

Homework

LPA and Wave Pinning Assignment