Self-Organized Criticality in Non-conserved Systems

Details Self-Organized Criticality in Non-conserved Systems Self-Organized Criticality in Non-conserved Systems

1994-07-19

arxiv.org/abs/cond-mat/9407082v1

Physics

Condensed Matter

11 pages, 4 separate figures, REVTEX

Scientific paper

10.1103/PhysRevLett.74.742

The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic and neutrally stable. A change to open boundaries results in the invasion of the interior by a ``self-organized'' region. The mechanism for the self-organization is closely related to the synchronization or phase-locking of the individual elements with each other. A simplified model of marginal oscillator locking on a directed lattice is used to explain many of the features in the non-conserved model: in particular, the dependence of the avalanche-distribution exponent on the conservation parameter $\alpha$ is examined.

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