Processes of Self-Assembly of Trees with Dependent Connections

Results obtained earlier for processes of self-assembly of segments [A. M. Leontovich, Probl. Peredachi Inf., 1975, vol. 11, no. 4, pp. 97–105] are generalized to processes of self-assembly of trees with intensities of tree formation and breakage that depend on which trees are combined and which are obtained after breakage respectively. The system of differential equations satisfied by the connection concentrations is obtained. Processes of self-assembly of trees that break down into nests are introduced. An invariant state manifold is obtained in the phase space of a dynamic system that describes disintegrating processes of self-assembly of trees.