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Here are a bunch of Problems for Romeo and Juliet (kindly appropriated
from Strogatz). Do the first one and try one more of the last four.
Consider the affair described by
- Characterize the romantic styles of Romeo and Juliet
- Sketch R(t) and J(t) starting at R(0)=1, J(0)=1.
- Try to sketch a rough phase portrait for this problem over the
range -2<R<2, -2<J<2. then
use STELLA to check your guess (hint: use the ``sensi specs'' to
do a series of runs across phase space).
- Classify the fixed point at the origin.
For one of the following problems, predict the course of the love
affair, depending on the signs and relative sizes of a and b If
you get stuck, just pick some arbitrary values for a and b and
use Stella to test your guesses. The question is how to understand
how the parameters might change the overall behavior of the
- (Out of touch with their own feelings) Suppose Romeo and Juliet
react to each other, but not to themselves: ,
- (Fire and water) Do opposites attract? Analyze ,
- (Peas in a pod) If Romeo and Juliet are romantic clones ( ,
), should they expect boredom or bliss?
- (Romeo the robot) Nothing could ever change the way Romeo
feels about Juliet: ,
. Does Juliet end up loving him or hating him?
Mon Sep 22 21:30:22 EDT 1997