Dynamics of Small Autocatalytic Reaction Networks II: Replication, Mutation and Catalysis

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.