Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 38. no. 1. pp. 106–130. ISSN 2079-6641

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MSC 37N35

Research Article

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

E. P. Okhapkina1,2, R. V. Meshcheryakov3, A. O. Iskhakova3, A. Y. Iskhakov3,4

1Russian State University for the Humanities, 125047, Moscow, Miusskaya Square 6, Russian Federation
2Bauman Moscow State Technical University, 105005, Moscow, 2nd Baumanskaya str., 5, build. 1, Russian Federation
3V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997, Moscow, Profsojuznaja Street 65, Russian Federation
4Moscow Institute of Electronics and Mathematics (MIEM HSE), 123458, Moscow, Tallinskaya str., 34, Russian Federation

E-mail: lenaokhapkina@mail.ru

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.

Key words: differential equations, social network communities, system dynamics, stability testing, experiment planning.

DOI: 10.26117/2079-6641-2022-38-1-106-130

Original article submitted: 19.03.2022

Revision submitted: 21.04.2022

Funding. The reported study is funded by RFBR according to the research project No. 18-29-22104 «Development of socio-cyberphysical system of monitoring of diverse Internet-content for counteraction to manifestation of aggression, pressure and other forms of destructive impact on individual and group consciousness of users»

For citation. Okhapkina E.P., Meshcheryakov R. V., Iskhakova A. O., Iskhakov A. Y. On the issue of stability of the dynamic system of functioning of social network communities. Experiment with a model. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 38: 1, 106-130. DOI: 10.26117/2079-6641-2022-38-1-106-130

Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Okhapkina E.P. et al., 2022

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Elena Pavlovna Okhapkina – Senior Lecturer Of Information Technologies And Systems Dep. Institute For Information Sciences And Security Technologies Of RSUH; Senior Lecturer Bauman Moscow State Technical University, Moscow, Russia ORCID 0000-0002-2382-0891.

Roman Valerievich Meshcheryakov – Doctor of Technical Sciences, Professor of the Russian Academy of Sciences, Chief Researcher of the V.A. Trapeznikov Institute of Management Problems of the Russian Academy of Sciences, Moscow, Russia, ORCID 0000-0002-1129-8434.

Anastasia Olegovna Iskhakova – Candidate of Technical Sciences, Senior Researcher, V.A. Trapeznikov Institute of control sciences of Russian Academy of Sciences, Moscow, Russia, ORCID 0000-0001-8358-298X.

Andrey Yunusovich Iskhakov – Candidate of Technical Sciences, Senior Researcher, V.A. Trapeznikov Institute of control sciences of Russian Academy of Sciences; Associate Professor of MIEM HSE, Moscow, Russia, ORCID 0000-0002-6603-265X.

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