Complex Systems

Parametric S-tree Method and Its Generalizations Download PDF

Karen M. Bekarian
Department of Applied Mathematics,
Yerevan State University,
A. Manugian 1,
Yerevan, Armenia

Anahit A. Melkonian
Theoretical Department,
Yerevan Physics Institute,
Alikhanyan Brothers str.2,
Yerevan, 375036, Armenia


A parametric approach is developed to the method of S-tree diagrams and its generalization for investigation of the hierarchical substructure of N-body nonlinearly interacting systems (e.g., clusters of galaxies). The introduction of a parametric function allows us to take into account the individual features of the particles which do not have a direct influence on the dynamics of the system but are crucial for analyzing the output data. An algorithm is proposed for the latter based on the construction of parametrical subgroups.

A generalization of the S-tree scheme is presented as well. This enables us to perform parallel substructure analysis with respect to various dependent or independent parameters, thus using fully the initial information of a system.