Finite-size effects of avalanche dynamics

Christian W. Eurich, J. Michael Herrmann, Udo A. Ernst

Research output: Contribution to journalArticlepeer-review


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 N⃗ ∞, 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.
Original languageEnglish
Number of pages15
JournalPhysical Review E
Publication statusPublished - 1 Dec 2002

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