Dynamics of Autocatalytic Replicator Networks Based on Higher Order Ligation Reactions

A class of autocatalytic reaction networks based on template dependent ligation and higher order catalysis is analyzed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The over-all dynamics can be understood by means of replicator equations with highly non-linear interaction functions. The dynamics depends crucially on the total concentration c0 of replicating material.