Scale invariance and invariant scaling in a mixed hierarchical system

We consider a mixed hierarchical model with heterogeneous and monotone cond itions of destruction. We investigate how scaling properties of defects in the model are related with heterogeneity of rules of destruction, determine d by concentration of the mixture. The system demonstrates different kinds of criticality as a general form of system behavior. The following forms of critical behavior are obtained: stability, catastrophe, scale invariance, and invariant scaling. Different slopes of the magnitude-frequency relation are realized in areas of critical stability and catastrophe. A simple rela tion between the slope of magnitude-frequency relation and parameters of th e mixture is established, [S1063-651X(99)08610-9].