Correlations in the Bak-Sneppen model from detrended fluctuation analysis

The correlations in the Bak-Sneppen (BS) model are studied from fluctuations of three variables with detrended fluctuation analysis method. Similar scaling behaviors of the detrended fluctuations are found for the series of the minimum fitness in one- and two-dimensional (1D and 2D) BS models. The root mean square detrended fluctuations increase in a power-law with the box size. For the series of the location of the minimum fitness and the number of active sites, the detrended fluctuations increase first for small box sizes and then saturate for large box sizes. The power spectrum for the series of the number of active sites is shown to be a typical 1/f behavior for both the 1D and 2D BS models.