Fluctuations and correlations in two-dimensional Bak$ndash$Sneppen model

Abstract

The self-organized criticality in the two-dimensional Bak–Sneppen model is studied from the fluctuations of the mean fitness and the jump of the minimum sites. An ensemble having the same number of updates from the initial state is used in the investigation. From the Gaussian distribution of the mean fitness in the ensemble, the lattice size dependence of the ensemble-averaged fitness is found. From the dependence, a solution to the gap equation is found and the critical gap and an exponent are calculated. A spatial–temporal correlation function is investigated from the jump of the minimum site.