Power law sensitivity to initial conditions for abelian directed self-organized critical models

The power law sensitivity to initial conditions is investigated for self-organized critical (SOC) models within the damage spreading framework. A class of two-dimensional abelian directed models are analyzed. Results for the time evolution of the normalized squared euclidian distance indicate that the propagation of a small perturbation (damage) has the same behavior even assuming different parameters of these models. The same technique, applied to a non-abelian complete toppling version of a directed model, leads to a completely different behavior. Results also suggest that there might exist a connection between the multifractal spectra of a potential energy measure and the power law sensitivity to initial conditions for the abelian SOC models, as observed for low-dimensional systems.