Presentation of project results on April 27 in class
Written report due on April 30 by email

I will ask you to explain the biological problem; formulate a model or find an existing one and in either case explain it in detail; show pictures of the interesting things that can be obtained from the model; and do as much of either the analysis or the simulations as you can. In most interesting cases the mathematical problem (either analytical or numerical) can be quite challenging, but you do know enough to attempt it in most cases.

Many of the suggested project themes have a dedicated chapter in all books that we have used. I mostly refer here to Murray's ``Mathematical biology book'' that has the most complete treatment of these topics. It is on hold in the library and parts of it are available on google books. However, you don't have to use the book as your main source of information or at all.

1.In the visual hallucinations model, explain and show the emergence of more interesting patterns such as in figures 9 and 10 of Ermentrout and Cowen (1979) (or 12.13 and 12.14 of Murray's book). Update: see also a brief comment on p. 540 of EK. Here is the Ermentrout cowen paper

2. Formation of occular dominance columns in the primary visual cortex (a possibe starting point is section 12.2 and problem 2 on p. 659 of Murray's book). Update: a similar problem is described as project 21 in dV, but you don't have to use a cellular automaton model as they suggest.

3. Spiral waves in a chemical reaction or scroll waves in the heart modelled with Barkley model (starting point: href="http://www.scholarpedia.org/wiki/index.php?title=Barkley_model&redirect=no and section 1.8 of Murray)

4. Development of mollusc shell patterns (section 12.4 of Murray as a possible start). Update: a good reference is The Algorithmic Beauty of Sea Shells which is available from the library . There is also a version of this problem (approached with cellular automata models) in dV project 24

5. Tumor growth (chapter 11 in Murray, several sections in Britton ``Essential mathematical biology''). Update: Possible train of thought is outlined in dV project 23 and can be combined with section 8.3 of Br

6. Re-invasion of sea-otters to California's coast. Update: This is project 18 of dV