A stochastic theory for temporal fluctuations in Self-Organized Critical systems.

Details A stochastic theory for temporal fluctuations in Self-Organized Critical systems. A stochastic theory for temporal fluctuations in Self-Organized Critical systems.

Dec 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agufmsm51b0536r&link_type=abstract

American Geophysical Union, Fall Meeting 2007, abstract #SM51B-0536

Mathematics

Probability

4480 Self-Organized Criticality

Scientific paper

In this work we use a mean field assumption to derive simple stochastic differential equation for the toppling activity in the Bak-Tang-Wiesenfeld (BTW) sandpile models, modelling the activity as an anti persistent fractional Brownian "super-walk", where the diffusion coefficient is proportional to the activity level itself. Through analysis of the stochastic differential equation and analytical solutions of the corresponding Fokker- Planck equation it is possible predict all the essential statistical properties of the toppling signal, including its spectral properties and the probability density functions for duration-times and the fluctuations in the signal itself. The methods used are insensitive to the particular details of the BTW class models, and can easily be modified to include other sandpile models.

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