Impact of composition on the dynamics of autocatalytic sets

Autocatalytic sets are sets of entities that mutually catalyse each other's production through chemical reactions from a basic food source. Recently, the reflexively autocatalytic and food generated theory has introduced a formal definition of autocatalytic sets which has provided promising results in the context of the origin of life. However, the link between the structure of autocatalytic sets and the possibility of different long-term behaviours is still unclear. In this work, we study how different interactions among autocatalytic sets affect the emergent dynamics. To this aim, we develop a model in which interactions are presented through composition operations among networks, and the dynamics of the networks is reproduced via stochastic simulations. We find that the dynamical emergence of the autocatalytic sets depends on the adopted composition operations. In particular, operations involving entities that are sources for autocatalytic sets can promote the formation of different autocatalytic subsets, opening the door to various long-term behaviours.