In a computer experiment we now simulate a decision which would change at a given
instant of time the value of the z-variable by an amount of less than a tenth of
a percent. This
impact is too small to be visible on the graph of fig.3. The results of
this new simulation is shown in figs.4a,b:
Fig.4a shows a super-position of the original z-variable (starting at
) and the z-variable of
the perturbed solution (starting at 
). As mentioned above, the time history for both solutions is
basically the same for about 200 time steps (about 10 intrinsic cycles of the
system
which is a more characteristic time unit than the algorithm dependent numerical
time-step). Later on, the difference between the two curves increases until they have
a basically independent evolution.
In fig.4b we have the corresponding plot for the x variable, which is basically uncorrelated with the z-variable. Nevertheless we can see that after somewhat over 200 time steps the two scenarios can have values which are completely (order unity) different from each other.
[htbp] (lorenz.2.eps scaled 695)
Super-position of the original z-variable and the z-variable of
the perturbed solution z'. Initially the difference is only 0.01, i.e. less
than 0.1%.
(b) Super-position of the original x-variable and the x-variable of the
perturbed solution x'.