Chirality Selection Models in a Closed System
  Recently the first chemical systems which show the amplification of enantiometric excess (ee) was found. Inspired by these experiments, we propose a few chemical reaction models in a closed system. The reactions consist of autocatalytic production of chiral molecules and their decomposition processes. By means of flow diagrams in the phase space of enatiometric concentrations, chiral symmetry breaking is studied.   Without any destruction processes, the quadratic autocatalysis leads to the amplification of ee, but the flow is attracted to a fixed line, which is only marginally stable. The destruction processes alter the attractor structure completely. With a cross inhibition the linear autocatalysis is sufficient for the chiral symmetry breaking with a complete homochirality. With a back reaction, the quadratic autocatalysis is necessary to bring about the chiral symmetry breaking. The final ee is not complete if there is a racemization process. 
Yukio Saito and Hiroyuki Hyuga