Heriot-Watt Mathematics Report Series
HWM02-19, 22 May 2002
Measurements of criticality in the Olami-Feder-Christensen model
G Miller and C J Boulter
Abstract
The Olami-Feder-Christensen model is a simple lattice based
cellular automaton model introduced as a prototype to study
self-organization in systems with a continuous state variable.
Despite its simplicity there remains controversy over whether the
system is truly critical in the non-conservative regime. Here we
address this issue by introducing the layer branching rate, which
measures how contributions to the system branching rate vary
across the lattice. By considering this quantity for layers far
from the edges of the finite-sized lattices we find that
the model is only critical in the conservative limit, but that
previous studies have underestimated the system branching rate in
the non-conservative case. We further derive expressions for the
branching rate in systems where the state variable across the
lattice is described by a uniform distribution, in order to
determine the effect of self-organization upon the level of
criticality. We find that organization raises the branching rate
in the nearest-neighbor case, but in contrast lowers the level of
criticality in a random-neighbor model.
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