  To understand the effects of fluctuations on achieving homochirality, we
employ a Monte-Carlo method where autocatalysis and enantiomeric
cross-inhibition, as well as racemization and deracemization reactions are
included. The results of earlier work either without autocatalysis or without
cross-inhibition are reproduced. Bifurcation diagrams and the dependencies of
the number of reaction steps on parameters are studied. In systems with 30,000
molecules, for example, up to a billion reaction steps may be needed to achieve
homochirality without autocatalysis.
