Basin of attraction of a bounded self-organized critical state

The robustness of the self-organized critical (SOC) state observed in the motion of an annular plate rotating over a granular medium is studied in this paper. In particular, we investigate the effect of parameters to which the emergent SOC state may be sensitive, including the initialization scheme, driving velocity, and confining pressure. The results indicate that the critical state is not a universal attractor, but has a finite basin of attraction. Furthermore, this state is only one of the three observed, which compare well with subcritical, critical, and supercritical states. The results call into question the precise definition of the term "self-organized criticality,'' an issue we address.