a) This system of equations is not linear. Locate the non-linear term. Then, find out how many critical points are there and their location.

b) Starting at the point (2,2,2), make a plot of the solution in the [t,x] plane, letting run t from 0 to 100.

c) Modify the previous plot to display the solution that starts at (2,2,2) in blue and a nearby solution in red starting at the point (2,2+a,2). Make plots for a equal to .1 , .01 , .001 , ... , .0000001

d) Make a table that relates the number of zeroes in a with the time elapsed until the two graphs divert from each other. You will have to make up a criterion to decide when the blue and red lines start to disagree significantly; just stick to the same criterion for the six plots.
Suppose you were to plot the solutions starting at (2,2,2) and (2,2.00...001,2) (where there are 100 zeroes). Can you use the table to predict how long will it take until these two curves diverge apart from each other?

e) Plot a graph of the solution starting at (2,2,2) in the x,y,z coordinates. An important component of your grade in this project is your description of the object that appears in your screen. Where are the critical points? How do the different trajectories mix? Why is there "chaos" in the picture?

Project due December 18, 2000.
Rodrigo Perez