  To study the dynamics of chemical processes, we often adopt rate equations to
observe the change in chemical concentrations. However, when the number of the
molecules is small, the fluctuations cannot be neglected. We often study the
effects of fluctuations with the help of stochastic differential equations.
  Chemicals are composed of molecules on a microscopic level. In principle, the
number of molecules must be an integer, which must only change discretely.
However, in analysis using stochastic differential equations, the fluctuations
are regarded as continuous changes. This approximation can only be valid if
applied to fluctuations that involve a sufficiently large number of molecules.
In the case of extremely rare chemical species, the actual discreteness of the
molecules may critically affect the dynamics of the system.
  To elucidate the effects of the discreteness, we study an autocatalytic
system consisting of several interacting chemical species with a small number
of molecules through stochastic particle simulations. We found novel states,
which were characterized as an extinction of molecule species, due to the
discrete nature of the molecules. We also observed a strong dependence of the
chemical concentrations on the size of the system, which was caused by
transitions to the novel states.
