Homework #7 for 445
Due: March 17, 2006
Read Chapter 6 of Meerschaert
Exercises from the text (Meerschaert)
1. Section 6.5, Problem 11.
2. Section 6.5, Problem 20.
3. Review the combat example in Section 6.1.
(If you prefer an application other than war, you can think of this as a model of antibodies
fighting a virus)
a) Write a code which does the discrete simulation of the combat, as given in equation (3)
on p. 195. Use this code to verify the critical value of λ which marks the division between red
or blue victory.
b) What happens if you run your code from part a) for a long time? At which point is the
result unrealistic?
c) Compare and contrast the behavior you observed in part b) with the simulation of the
continuous analogue of the model:
dx1
= −λa1 x2 − b1 x1 x2
dt
dx2
= −λa2 x1 − b2 x1 x2
dt
Do you find the same critical value of λ dividing red and blue victory as in part a)? Do you
encounter the same problem as in part b) for long time solutions?
4. Your proposals for the Final Project are also due on March 17.