  We demonstrate that the chaotic nature of N-body systems can lead to
macroscopic variations in the evolution of collisionless simulations containing
rotationally supported discs. The unavoidable stochasticity that afflicts all
simulations generally causes mild differences between the evolution of similar
models but, in order to illustrate that this is not always true, we present a
case that shows extreme bimodal divergence. The divergent behaviour occurs in
two different types of code and is independent of all numerical parameters. We
identify and give explicit illustrations of several sources of stochasticity,
and also show that macroscopic variations in the evolution can originate from
differences at the round-off error level. We obtain somewhat more consistent
results from simulations in which the halo is set up with great care compared
with those started from more approximate equilibria, but we have been unable to
eliminate diverging behaviour entirely because the main sources of
stochasticity are intrinsic to the disc. We show that the divergence is only
temporary and that halo friction is merely delayed, for a substantial time in
some cases. We argue that the delays are unlikely to arise in real galaxies,
and that our results do not affect dynamical friction constraints on halo
density. Stochastic variations in the evolution are inevitable in all
simulations of disc-halo systems, irrespective of how they were created,
although their effect is generally far less extreme than we find here. The
possibility of divergent behaviour complicates comparison of results from
different workers.
