Parallel Bak-Sneppen model and directed percolation

We introduce a parallel version of the Bak-Sneppen model that is rigorously shown to evolve spontaneously to a site directed percolation critical point. This exemplifies the mechanism underlying a class of self-organized critical models, in which self-organized criticality can be traced back to the existence of an underlying dynamical critical point. This critical point can be reached either by tuning a control parameter or by driving the system infinitely slowly (i.e., by going at a very small rate of evolution). An alternative dynamical evolution formulation of the parallel version of the Bak-Sneppen model enables us to get a very precise estimation of the critical threshold for the corresponding directed percolation problem.