SUSTAINABILITY OF NATURAL PHENOMENA ON THE EXAMPLE OF SOCIO-ECONOMIC BIOSYSTEMS (SEB)
Author(s): Shapovalov A.B.
Rubric: Economics of sustainable development
DOI: 10.21777/2587-554X-2025-4-67-76
Release: 2025-4 (55)
Pages: 67-76
Keywords: socio-economic biosystem (SEB), sustainability, multidimensional space, digitalization, vector space of features, sets, natural phenomena
Annotation: The article examines the sustainability of natural phenomena, which determines the consistency of the perception of reality. An adequate example of research is the multidimensional and multiparametric socio-economic biosystem (SEB) as a carrier of the phenomenon of life. There is a rapid accumulation of information about all aspects of the multidi- mensional space of the SEB by digitalization. Based on this, the multidimensional space is mathematically formalized by the vector feature space. From this, the geometry of the multidimensional information space of the SEB is formed, which makes it possible to simulate both direct and inverse problems of analysis. The formalization of the geometry of the SEB multidimensional information space is regulated by 3 functionals that reflect socio-political, economic and biological (including medical) aspects in the form of geometric images. Projection of geometric images into spaces of lower dimensions makes it possible to interpolate and/or approximate numerical arrays of images of SEB functionals into an analytical form. The obtained analytical representation of SEB images provides an opportunity for traditional studies of their properties. In the 2-dimensional view (plane), the SEB is represented by canonical polynomials of various degrees. It is shown that the necessary and sufficient condition for the global stability of canonical polynomials is determined according to Hurwitz. It is noted that reducing the number of checks of determinant inequalities is possible by means of the Liénard – Chipart criterion and some other methods. An assessment of the global stability of the natural phenomenon of SEB according to Hurwitz is carried out. The results obtained reveal the potential of anthropogenic manageability (adaptation) of the SEB. The immanent modeling of reality using multidimensional information arrays extends the mathematical task of evaluating polynomial stability to the stability of a set.
Bibliography: Shapovalov A.B. SUSTAINABILITY OF NATURAL PHENOMENA ON THE EXAMPLE OF SOCIO-ECONOMIC BIOSYSTEMS (SEB) // Economics and Management. – 2025. – № 4 (55). – С. 67-76. doi: 10.21777/2587-554X-2025-4-67-76