Andy Long
Problem 3:
Lorenz defined his equations a little more generally than those which follow, using some parameters in place of the constants below (10, 28, 8/3). However these parameter values give equations which define a chaotic dynamical system:
Choose any three small real numbers (1, 2, and -3, say) as initial values for x, y, and z.
You need to tell STELLA that your variables can be negative: when you set the initial values, there is a checkbox (checked by default) indicating whether the variable is assumed negative or not. Make sure that it is not checked, or your simulations will be completely incorrect!
When I set this up, I got ridiculous results. I assume that I made an error in defining the system, but software can sometimes go awry.... See if you can do better! [By the way: how do you know if you know if you are getting garbage out? The answer: do the mathematics! Pushing buttons isn't enough sometimes....]
Compare the different solvers (i.e Euler, Runga Kutta 4). See if you can get any two plots to look the same in the long term (that is, for large time) when you change initial values (even by a tiny bit). The hallmark of a chaotic system is sensitive dependence on initial conditions: that is, if you change them just a hair, the solution will soon change so that it is unrecognizable from the other.