Abstract:

The fluctuations and correlations in the Bak-Sneppen model for self-organized criticality are discussed. By introducing the mean fitness of the system, one can discover the lattice size dependence of the ensemble-averaged fitness from the fluctuations. From the size dependence one can find a solution of the gap-equation and then get the exponents for the model. We also investigate the flying of the minimum site in the updating process. The distribution of the fly distance becomes more and more sharp at 0, which shows the increase of the correlation between the minimum sites at two successive updates. We link a spatial-temporal correlation function with the flying and get a simple expression for the correlation function.

Key words: Bak-Sneppen model, fluctuations, correlations