Branching process with dependent particles as a model of the catastrophic behavior

Recent studies showed that many of man-caused accidents and natural disasters are systemic. I.e. a catastrophic event occurs not because of the unfavorable concatenation of circumstances but owing to a taste for the catastrophic behavior inherent to complex systems. Power probability distribution laws are a mathematical image of catastrophicality. The universal system mechanism of theirs origin is a self-organization to the critical state which takes place in many open nonlinear systems. However particular processes resulting in power laws can be quite different. So the question arises as to the mutual relation of these processes and self-organization phenomenon. We investigate a branching process with dependent particles. It's characterized by power law and can be a model of the catastrophic behavior.