The Hypercycle

Topologic methods are used to characterize a particular class of self-replicative reaction networks: the hypercycles. The results show that the properties of hypercycles are sufficient for a stable integration of the information contained in several self-replicative units. Among the catalytic networks studied, hypercyclic organization proves to be a necessary prerequisite for maintaining the stability of information and for promoting its further evolution. The techniques used in this paper, though familiar to mathematicians, are introduced in detail in order to make the logical arguments accessible to the nonmathematician.