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Evolution of complex hierarchical systems is only partly determined by main stream which, in its turn, is defined by system potential, outside conditions and adequate top-level control actions. Random corrections, caused by low-level decisions based on self-made short-term and short-scale estimations, make system trajectory rather chaotic. A temporal behavior of such near-to-chaos system will correspond (in terms of nonlinear dynamics) not to the motion along a smooth manifold but to “infinitely fragmented” fractal set. So, the more complicated is the system motion, the higher becomes the fractal dimension of the attraction channel and the more unstable becomes the system. However, the systems in question are capable to self-organizing and so are capable to surviving. As results, these systems will restore the “directed” (according to the minimum dissipation principle) development due to adequate control through all level of hierarchy. So, the study of reguliarities of the attraction channel formation during the restoring of the “directed” development becomes reasonable to obtain better understanding of self-adjusting physics.
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