Systems analysis: Mathematical modeling and approach to structural complexity measure using polyhedral dynamics approach

Abstract

This research paper analyzes and proposes modification of the Polyhedral Dynamics procedure which is based on algebraic (and geometric) representation of a system 's structure as a simplicial complex. Mathematical analysis of complex refers to the studying of multidimensional chains of connectivity, and its results provide a background for measuring structural complexity. The term «complexity» is many-sided, and in the present paper it is examined through connectivity and relations between a system 's elements. As it is discussed, complexity of structure expressed in numeric form is non-informative, but even at the initial stage of analysis it becomes reasonable to express complexity linguistically, to fill the results of the mathematical modeling stage with meaning. The appropriateness of a sequential using of mathematical and logical models is considered.