  Based on the theory of hierarchical structures, a correspondence has been
established between the dynamics for the number of neutrons obtained from the
theory of branching processes, the number of neutrons of the n-th generation,
the number of nodes at the n-th level of the hierarchy, the rate of change in
the probability of a chain reaction, the type of intensity and strength of the
hierarchical connection, the degree reactor criticality, and neutron
trajectories in the reactor. A connection has been found between the
probabilities of the formation of a certain generation of the number of
neutrons and the probability of the occurrence of a self-sustaining chain
reaction of nuclear fission. It is shown that the Tsallis and R\'enyi
distributions describing these processes are related by relations of deformed
algebra, and under certain conditions can be accompanying with respect to each
other.
