Dynamics of Small Autocatalytic Reaction Networks II: Replication, Mutation
Peter F. Stadler, Wolfgang Schnabl, Christian V. Forst and Peter Schuster
Mutation is introduced into autocatalytic reaction networks. The differential
equations obtained are neither of replicator type nor can they be transformed
straightway into a linear equation. Examples of low dimensional dynamical
systems---$n= 2, 3 $, and 4---are discussed and complete qualitative analysis is
presented. Error thresholds known from simple replication-mutation kinetics
with frequency independent replication rates occur here as well. Instead of
cooperative transitions or higher order phase transitions the thresholds appear
here as supercritical or subcritical bifurcations being analogous to first
order phase transitions.
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