Critical transitions in colliding cascades

We consider here the interaction of direct and inverse cascades in a hierar chical nonlinear system that is continuously loaded by external forces. The load is applied to the largest element and is transferred down the hierarc hy to consecutively smaller elements, thereby forming a direct cascade. The elements of the system fail (i.e., break down) under the load. The smalles t elements fail first. The failures gradually expand up the hierarchy to th e larger elements, thus forming an inverse cascade. Eventually the failures heal, ensuring that the system will function indefinitely. The direct and inverse cascades collide and interact. Loading triggers the failures, while failures release and redistribute the load. Notwithstanding its relative s implicity, this model reproduces the major dynamical features observed in s eismicity, including the seismic cycle, intermittence of seismic regime, po wer-law energy distribution, clustering in space and time, long-range corre lations, and a set of seismicity patterns premonitory to a strong earthquak e. In this context, the hierarchical structure of the model crudely imitate s a system of tectonic blocks spread by a network of faults (note that the behavior of such a network is different from that of a single fault). Loadi ng mimics the impact of tectonic forces, and failures simulate earthquakes. The model exhibits three basic types of premonitory pattern reflecting sei smic activity, clustering of earthquakes in space and time, and the range o f correlation between the earthquakes. The colliding-cascade model seemingl y exhibits regularities that are common in a wide class of complex hierarch ical systems, not necessarily Earth specific.