Eur. Phys. J. B 82, 83-89 (2011)
https://doi.org/10.1140/epjb/e2011-10941-4

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

¹ Department of Physics, College of Science, Nanjing Forestry University, Nanjing, 210037, P.R. China
² Department of Physics, Faculty of Science, Ege University, 35100 Bornova, Izmir, Turkey
³ Department of Electronic Engineering, Fudan University, Shanghai, 200433, P.R. China
⁴ Department of Physics, Nankai University, Tianjin, 300071, P.R. China

Corresponding authors: ^a zhanggq@mail.nankai.edu.cn - ^b ugur.tirnakli@ege.edu.tr

Received: 1 December 2010
Revised: 18 April 2011
Published online: 29 June 2011

Abstract

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_add 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.