Finite-size effects of avalanche dynamics

Christian W. Eurich, J. Michael Herrmann, and Udo A. Ernst
Phys. Rev. E 66, 066137 – Published 31 December 2002
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Abstract

We study the avalanche dynamics of a system of globally coupled threshold elements receiving random input. The model belongs to the same universality class as the random-neighbor version of the Olami-Feder-Christensen stick-slip model. A closed expression for avalanche size distributions is derived for arbitrary system sizes N using geometrical arguments in the system’s configuration space. For finite systems, approximate power-law behavior is obtained in the nonconservative regime, whereas for N, critical behavior with an exponent of 3/2 is found in the conservative case only. We compare these results to the avalanche properties found in networks of integrate-and-fire neurons, and relate the different dynamical regimes to the emergence of synchronization with and without oscillatory components.

  • Received 14 September 2000

DOI:https://doi.org/10.1103/PhysRevE.66.066137

©2002 American Physical Society

Authors & Affiliations

Christian W. Eurich*

  • Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee 1, D-28334 Bremen, Germany

J. Michael Herrmann

  • Max-Planck-Institut für Strömungsforschung, Bunsenstrasse 10, D-37073 Göttingen, Germany

Udo A. Ernst

  • Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee 1, D-28334 Bremen, Germany

  • *Electronic address: eurich@physik.uni-bremen.de

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Vol. 66, Iss. 6 — December 2002

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