Critical behavior of a model for catalyzed autoamplification.

We examine the critical behavior of a model of catalyzed autoamplification inspired by a common motif in genetic networks. Similar to models in the directed percolation (DP) universality class, a phase transition between an absorbing state with no copies of the autoamplifying species A and an active state with a finite amount of A occurs at the point at which production and removal of A are balanced. A suitable coordinate transformation shows that this model corresponds to one with three fields, one of which relaxes exponentially, one of which displays critical behavior, and one of which has purely diffusive dynamics but exerts an influence on the critical field. Using stochastic simulations that account for discrete molecular copy numbers in one, two, and three dimensions, we show that this model has exponents that are distinct from previously studied reaction-diffusion systems, including the few with more than one field (unidirectionally coupled DP processes and the diffusive epidemic process). Thus the requirement of a catalyst changes the fundamental physics of autoamplification. Estimates for the exponents of the diffusive epidemic process in two dimensions are also presented.