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A solvable non-conservative model of Self-Organized Criticality

Gunnar Pruessner·Henrik Jeldtoft Jensen
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Abstract

We present the first solvable non-conservative sandpile-like critical model of Self-Organized Criticality (SOC), and thereby substantiate the suggestion by Vespignani and Zapperi [A. Vespignani and S. Zapperi, Phys. Rev. E 57, 6345 (1998)] that a lack of conservation in the microscopic dynamics of an SOC-model can be compensated by introducing an external drive and thereby re-establishing criticality. The model shown is critical for all values of the conservation parameter. The analytical derivation follows the lines of Broeker and Grassberger [H.-M. Broeker and P. Grassberger, Phys. Rev. E 56, 3944 (1997)] and is supported by numerical simulation. In the limit of vanishing conservation the Random Neighbor Forest Fire Model (R-FFM) is recovered.

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Gunnar Pruessner, Henrik Jeldtoft Jensen. 2001-04-30. A solvable non-conservative model of Self-Organized Criticality. https://doi.org/10.1209/epl%2Fi2002-00630-6

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