Crazy tic tac bounce!? | EVERYDAY MYSTERIES

I have a physics mystery that I have wondered about for years; if you spin a relatively tall cylinder, such as a beer bottle, (you can guess where I have played with this. :) ) on its lower edge, you can get it to roll around for quite a while before it either spins to a stop upright, or falls over. If you are at the right angle and spin rate, it seems to be unpredictable whether it ends up upright or falls.
My question is; is this an example of a chaotic system? It seems remarkably complex for something with such simple components.
(I've done some searches for papers on the subject, and there are quite a few on the physics of spinning cylinders, but they all seem to focus on what happens when it approaches the upright condition.)