Third Written Assignment

Due October 10 Math 375 Sadun/Ristov
 

Up to three people are urged to work together.  Please hand in only one assignment per group.
 

1. Make up a model of interaction for two species which are symbiotic.
One example of such an interaction is moss and lichen. (Or lichen itself,
which is a symbiote of two species).  This means that
the interaction between the two species helps both. Explain each term.

For such a model to be realistic, it needs to have a stable (and nonzero!) fixed point.  If your model has parameters, try tweaking them to see when such a stable fixed point exists.

2. Problem 5, page 102 from Taubes. This involves analysis of the
equations dx/dt = y - x*x; dy/dt = x - 1.

3. Problem 6, page 103 from Taubes. This involves analysis of the
equations dx/dt = 2y; dy/dt = x*x + y*y - 1.
 

4. (extra credit) Outline an experiment that could be used to determine
the constant a in the model for competition in chapter 5.

5.  (extra credit) Suppose that you have a bit of extra money come in,
left to you by an eccentric aunt, who split her estate between you and
her favorite charity. You find several options

Investment at 5% compounded yearly, insured by the FDIC.

Investment at 5% compounded daily, not insured, but with the University
Federal Credit Union.

Investment in bonds earning 5%, compounded continuously, issued by Microsoft.

Investment at 10%, compounded continuously, with a bank in Afghanistan.

If nothing goes wrong, how much will you have after 10 years in each
case?  Do you think your answers would be welcomed by the Kabul Chamber of Commerce?