PACE REPORT

Autocatalytic kinetics can be found in several replicator entities. In the context of general replicator theory we have explored the hypercycle dynamical system from several theoretical points of view. We have first explored the dynamical properties of simple, autocatalytic replicators by means of differential equations and cellular automata models considering stochasticity and spatial molecular dynamics. We have investigated the role of space and parasites in the asymptotic regimes of these systems.We have found that the asymmetry of the catalytic replicators as well as three spatial degrees of freedom are crucial for the survival of the entire catalytic network. These results are in agreement with the well-mixed, mean field models. We have also focused our analysis on the dynamical properties arising in the vicinity of the bifurcation points separating both survival and extinction phases.