A stochastic model of catalytic reaction networks

Autocatalytic networks are widespread in nature, but theyare diffcult to create or to reproduce in laboratory. There are however several models of coupled reactions which describe a phase transition to an autocatalytic cycle when a certain level of heterogeneity in the composition of the chemical soup is reached, so it is interesting to understand why these phenomena are not easily achieved in the laboratory. For this purpose we introduce here a model, inspired by a previous one by Kauffman, tailored for the study of such properties. In particular, we take intoaccount the stochastic nature of the dynamics of interacting molecules, in the case of a well stirred tank reactor. We describe the model and we analyse its behaviour under dierent circumstances. In particular, the onset of an autocatalytic set is studied as the feed is varied, and its stability is analysed