The study of the properties of structural models of elements of educational environment

Abstract

The widespread use of mathematical modeling is often constrained by the insufficient level of technological maturity and the lack of theoretical foundations to justify the effectiveness of different classes of models. One of the ways to improve educational project management systems is to solve problems of modeling the structure and trajectory of changes in the parameters of the system in education management, as a complex poorly structured organizational and technical system. To solve the problem of analysis of structural schemes of complex technical systems, which include education systems, it is proposed to use the analytical method of determining closed cycles in complex control systems. The method is based on the use of specific properties of adjacency matrices. It is shown that the degrees of the adjacency matrix follow the general structure of the oriented graph with certain regularities of mapping the arcs of the graph. This allows you to create a matrix of reach of the studied topological structure with the selection of contours in an oriented graph. A method for identifying cycles in graphs based on the formation of the Boolean sum of degrees of the reach matrix with its subsequent transposition and superposition has been developed, which allows obtaining a mapping of a contour in a graph in the form of a square submatrix filled with units.