Completely deterministic self-organized critical state of sandpile automaton models

Abstract

We study the general Abelian sandpile cellular automaton model of self-organized criticality in which the toppling conditions depend on the local height. We find that under some special kind of toppling rules, the self-organized critical states become completely deterministic, that is, the evolution of the system depends only on the total number of particles added to it but is totally independent of where you drop those particles. The results is quite general and can be applied to various models of self-organized criticality. The result has a close resemblance with the study of periodic behavior of circle maps in chaos.