Convergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models

The conventional Hamming distance measurement captures only the short-time dynamics of the displacement between the uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [Int. J. Mod. Phys. C 14, 805 (2003)] is used to study the short-time and long-time dynamics of the two distinct random configurations of the isotropic and anisotropic Bak-Sneppen models on a square lattice. Similar to 1-dimensional case, the time evolution of the displacement is intermittent. The scaling behavior of the jump activity rate and waiting time distribution reveal the absence of typical spatial-temporal scales in the mechanism of displacement jumps used to quantify the convergence dynamics.