On the issue of stability of the dynamic system of functioning of social network communities. experiment with the model

Social networks are no longer used only as a tool for global communication of various segments of society in different countries. It is turned into a socio-political asset in the struggle for the specific interests of a group of people who can acquire and/or manage this asset. In the paper we use data of a number of communities of the Russian-Ukrainian segment of the social network «Vkontakte». The study formalizes one of the functional features of a social network: a community (group). The article considers the dynamic system of functioning of social network communities and provides a set of numerical experiments to test the stability of a system of differential equations. The system is investigated for stability by the method of Lyapunov functions. The zone of permissible values of dynamic system parameters is determined. As a result of numerical solutions of a system of nonlinear equations with a parameter controlling the dynamics of the system, results comparable to theoretical ones were obtained, and, despite some inaccuracies, sufficiently well describing the features of the dynamics of the system under consideration.