AUTOCATALYTIC NETWORKS WITH INTERMEDIATES .1. IRREVERSIBLE REACTIONS

A class of autocatalytic reaction networks based on template-dependent replication and specific catalysis is considered. Trimolecular ''elem entary steps'' of simple replicator dynamics are resolved into two con secutive irreversible reactions. The extreme cases, competition for co mmon resources and hypercycle-like cooperative feedback, were analyzed in some detail. Although the dynamics of the extended networks resemb les corresponding replicator dynamics in general, there are significan t differences. Most notably, the interior fixed points in the cooperat ive model turned out to be asymptotically stable for an arbitrary numb er of species, whereas simple replicator dynamic predicts an asymptoti cally stable periodic orbit fixed for four species and fewer and a sta ble periodic orbit for all other cases. (C) Elsevier Science Inc., 199 7.