Chiral symmetry breaking: (i) limited enantioselectivity and (ii) mutual inhibition

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized geometrically and analytically. The first model accounts for limited enantioselectivity, while the second is the Frank model in which the mutual inhibition reaction is allowed to be reversible. Both models include the autocatalytic amplification of units of the same chirality as well as chiral inhibition, in unison regarded to be the elementary requirements for achieving symmetry breaking of initially racemic mixtures. When the control parameter for each model falls below its corresponding critical value, the racemic state becomes unstable, and chiral amplification results. These final stable chiral states are not homochiral: mirror symmetry is broken, but the breaking is not absolute. Numerical solutions are obtained in two space dimensions.