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

The limited roles of autocatalysis and enantiomeric cross inhibition in achieving homochirality in dilute systems