Criticality in a dynamic mixed system - art. no. 056123

We suggest a dynamic generalization of the simplest static hierarchical mix ed model introduced by Shnirman and Blanter [Phys. Rev. Lett. 81, 5445 (199 8); Phys. Rev. E. 60. 5111 (1998). We show that the stationary solution of the dynamic mixed model (DMM) demonstrates, in general, a linear form of th e magnitude-frequency relation and may be considered a self-organized criti cal system. The dynamic mixed model demonstrates three principal kinds of s ystem behavior: stability, catastrophe. and scale invariance. We show that the catastrophic area exists for all parameters of the mixture. and obtain three analytical expressions for boundary conditions of the stability and t he scale invariance domains. As in the static model scale invariance appear s as a result of a strong heterogeneity of the mixture. We describe how the magnitude-frequency relation reflects parameters of the heterogeneity and heating conditions for different domains of system behavior. Deviation of t he DMM from the static mixed model and possible applications to earthquake prediction are discussed.