We numerically and analytically investigate two self-organized critical sandpile models with anisotropic dynamics of the activity propagation – Dhar–Ramaswamy and discrete Feder–Feder models. The full set of critical indices for these models is theoretically determined. We also give systematic description of the finite-size scaling method and its use for the solving of self organized critical systems. Studding the discrete Feder–Feder model we find and explain a number of nontrivial phenomena, such as spontaneous anisotropy, anomalous diffusion and the appearance of midline ditch of filling.

self-organized criticality, sandpile models, scale invariance, power laws, finite-size scaling, anomalous diffusion, spontaneous anisotropy

Mathematical modelling in actual problems of science and technics