Self-Organized Criticality in a Mixed Hierarchical System

It is demonstrated that the self-organized criticality emerges in a hierarchical system as a result of heterogeneity in the scaling conditions. A heterogeneous system consisting of a mixture of the simplest hierarchical models of failure is considered. Four types of model behavior are obtained: stability, catastrophe, unstable criticality, and stable (self-organized) criticality. It is shown that the self-organized criticality reflects heterogeneous properties of media. Possible applications to the study of seismicity are discussed.