title: Finite-size effects of avalanche dynamics.
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--> infinity, 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.
authors.affiliation: Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee 1, Germany. eurich@physik.uni-bremen.de
authors.forename: Christian W
authors.initials: CW
authors.lastname: Eurich
authors.forename: J Michael
authors.initials: JM
authors.lastname: Herrmann
authors.forename: Udo A
authors.initials: UA
authors.lastname: Ernst