Difference between revisions of "Modeling: Pattern formation using Reaction-Diffusion models"
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# turing53chemical pmid=2185858 [http://links.jstor.org/sici?sici=0080-4622%2819520814%29237%3A641%3C37%3ATCBOM%3E2.0.CO%3B2-I pdf file] | # turing53chemical pmid=2185858 [http://links.jstor.org/sici?sici=0080-4622%2819520814%29237%3A641%3C37%3ATCBOM%3E2.0.CO%3B2-I pdf file] | ||
</biblio> | </biblio> | ||
| + | A short treatment in, Farkas, Dynamical Models in Biology, Academic Press, 2001 [[Media: FarkasA3.3.pdf]] | ||
== Mathematical background == | == Mathematical background == | ||
See the [[Introduction to dynamical systems and differential equations]] | See the [[Introduction to dynamical systems and differential equations]] | ||
| − | + | [[Media: FarkasA3.3.pdf]] | |
---- | ---- | ||
(Project in [[Course: "Solving Biological Problems that require Math"]]) | (Project in [[Course: "Solving Biological Problems that require Math"]]) | ||
Revision as of 17:36, 23 March 2009
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>
- turing53chemical pmid=2185858 pdf file
</biblio> A short treatment in, Farkas, Dynamical Models in Biology, Academic Press, 2001 Media: FarkasA3.3.pdf
Mathematical background
See the Introduction to dynamical systems and differential equations Media: FarkasA3.3.pdf
(Project in Course: "Solving Biological Problems that require Math")
