Sensitivity to initial conditions in self-organized critical systems

Details Sensitivity to initial conditions in self-organized critical systems Sensitivity to initial conditions in self-organized critical systems

2003-06-25

arxiv.org/abs/cond-mat/0306647v2

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, submitted to Physical Review Letters

Scientific paper

10.1007/s10955-004-5709-3

We discuss sensitivity to initial conditions in a model for avalanches in granular media displaying self-organized criticality. We show that damage, due to a small perturbation in initial conditions, does not spread. The damage persists in a statistically time-invariant and scale-free form. We argue that the origin of this behavior is the Abelian nature of the model, which generalizes our results to all Abelian models, including the BTW model and the Manna model. An ensemble average of the damage leads to seemingly time dependent damage spreading. Scaling arguments show that this numerical result is due to the time lag before avalanches reach the initial perturbation.

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