Autocatalytic Networks with Intermediates I: Irreversible Reactions
Robert Hecht, Robert Happel, Peter Schuster, and Peter F. Stadler
A class of autocatalytic reaction networks based on template dependent
replication and specific catalysis is considered. Trimolecular "elementary
strps" of simple replicator dynamics are resolved into two consecutive
irreversible reactions. The extreme cases, competition for common resources
and hypercycle-like cooperative feedback, were analyzed in some detail.
Although the dynamics of the extended networks resembles corresponding
replicator dynamics in general, there are significant differences.
Most notably, the interior fixed points in the cooperative model turned to be
are asymptotically stable for an arbitrary number of species whereas simple
replicator dynamics predict an asymptotically stable fixed for four species
and less and a stable periodic orbit for all other cases.
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