Studies of scale invariant change-over dynamics
in the hierarchical model of defects development
Hierarchical model of defects development makes possible the consideration of both ordinary and self-organized criticality from the common viewpoint. Scale invariant critical state in this model is presented by fixed points of a renormalization transformation, connected with lifting to the next level of hierarchy. So stable fixed points of the transformation correspond to the self-organized criticality and unstable points correspond to the ordinary one.
We supplement the renormalizational approach to the critical state with the dynamical one, which is more usual to the theory of self-organized criticality. We show that singular disturbances at the lowest level of hierarchical system result in the power-law distributed response. We investigate the dependence of distribution indices on the model parameters.
Mathematical modelling in actual problems of science and technics