I prefer phase portraits: plotting trajectories with the axes being
the state variables. Even projecting from a 4-d system to a 2-d
system, you should see the behavior settling down to some fixed
orbit, though it may appear to cross itself in the projectiong.
(I think you're better off with a variable step-size algorithm.)
Let the simulation run a fairly long time and plot, but save the
full 4-d (5-d with time [?]) data set. If it's settles down by the
end. Use the final condition as a starting condition for another
sim. and just look at the tabulated output. You should see the
'pattern.' Then you can pick one point on the trajectory and
construct your return map around that.
A software source (including much free- and share- ware) is
http://archives.math.utk.edu/software.html
It's categorized. I have a couple more that might be useful on
my web 'maths' page (http://www.netcom.com/~drpauls/maths.html),
but it won't load right now and someone else mentioned having
trouble connecting. I may be moving from Netcom soon if they
don't upgrade the service.
-Paul
