Modeling: Pattern formation using Reaction-Diffusion models

Background: One of the most amazing properties of biological systems is their ability to form complex and organized structures. Those structures range from simple patterns (like the stripes of a zebra) to highly complex constructs (like a cell). How such structures or patterns can emerge by themselves remains a largely unsolved problem. In this project, we investigate how a simple pattern can emerge in a decentralized manner, without any plan.

Goal: The goal of the project is to understand and analyze (with computer simulations) one of the simplest and most influential pattern formation mechanism using Reaction-Diffusion models.

Mathematical tools: This project uses partial differential equations. A short introduction to partial differential equations will be provided. A mathematical software for performing simulations (matlab) will also be used.

Biological or Medical aspects: It will be investigated to which extend this model can explain the patterns observed on animals such as leopards or zebras.

Supervisor: Micha Hersch

Presentation: Media:Micha.ppt

Students: Christophe Seppey and Balazs Laurenczy

References:

The pioneering paper from Alan Turing <biblio>

1. turing53chemical pmid=2185858 pdf file

</biblio>

Mathematical background

See the Introduction to dynamical systems and differential equations

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(Project in Course: "Solving Biological Problems that require Math")