Group Assignments

Using the analytical, graphical and numerical methods we have learned this semester, investigate one of the following systems and describe

• its steady states (equilibria)
• the stability of the steady state(s) and any bifurcations which occur as the parameter(s) is(are) varied
• the asymptotic, time-dependent or -independent behavior of the system, generally determined by numerical methods

For the graphical and numerical investigations, you can use either MATLAB or MAPLE or any other software with which you feel comfortable. The entire project is worth 30 points, 5 of which will be an average of points distributed by group members to other members of their own group.

• Written Component (15 points)
  Each group should turn in a written summary which includes:
  1. a brief (2-4 paragraph) summary of the scientific concepts which are being modeled by the system of ODEs
  2. a clear summary of the steady state analysis, including bifurcations and stability properties
  3. printouts from any numerical analyses you have carried out, including phase plane plots and a summary of the dependence of solution behavior on parameter values
• Oral Component (10 points)
  Each group should devise a way to present orally the contents of the project to the rest of the class. This may be done by one designated spokesperson or by a group effort. The presentations will be done in the computer lab and the group may use the project screen, attached to a computer, to present results of numerical solutions, etc.
• Project Topics
  1. Predator-prey model
  2. Glycolysis reaction
  3. Cell division cycle
  4. Oscillating chemical reaction
  5. AIDS treatment