Self organized criticality in a modified Olami-Feder-Christensen model

摘要

A modified version of the Olami-Feder-Christensen model has been introduced to consider avalanche size differences. Our model well demonstrates the power-law behavior and finite size scaling of avalanche size distribution in any range of the adding parameter p _{a d d} of the model. The probability density functions of the avalanche size differences at consecutive time steps (defined as returns) appear to be well approached, in the thermodynamic limit, by q-Gaussian shape with appropriate q values which can be obtained a priori from the avalanche size exponent τ. For small system sizes, however, return distributions are found to be consistent with the crossover formulas proposed recently in Tsallis and Tirnakli [J. Phys. Conf. Ser. 201, 012001 (2010)]. Our results strengthen recent findings of Caruso et al. [Phys. Rev. E 75, 055101(R) (2007)] on the real earthquake data which support the hypothesis that knowing the magnitude of previous earthquakes does not make the magnitude of the next earthquake predictable.