Methodological aspects of the analysis for stability of small social systems

Abstract

This article develops a comprehensive methodology for analyzing stability of small social systems, which are considered fundamental, self-regulating units of a society. In today's highly dynamic and unstable socioeconomic environment, sustainability of these basic structures is of paramount importance. This paper examines a small social system through the state of three key interrelated characteristics: the material component, which represents the resource base; the information and communication component, which determines the quality of data exchange and the level of social tension; and the energy component, which reflects the level of psychophysiological resources and motivation of participants. To assess each of these com ponents quantitatively, the method for integrated indicators is proposed, aggregating the weighted values of relevant primary metrics. The primary tool for visualization and holistic analysis is the construction of a phase portrait of the system in a three-dimensional space formed by integrated indicators, which allows for identifying zones of high and low system functionality. The quantitative criterion for stability is the dynamics of parameter dispersion in this phase space, estimated using the principal component analysis (PCA), where the measure of dispersion is the sum of the eigenvalues of the covariance matrix. The proposed methodology was tested using a small enterprise team as a case study, demonstrating its practical applicability. The identified oscillatory dynamics of the total variance, with a tendency toward parameter concentration, is interpreted within the framework of catastrophe theory as a sign of a stable but adaptable system state. The developed approach provides the researcher with an integrated toolkit for moving from qualitative description to quantitative diagnostics and monitoring of the resilience of small social systems.