The problem of preventive risk management in "smart communities" based on stochastic simulation

Objectives. The study aims to analyze the problem of preventive risk management for problematic situations and incidents in the functioning of "smart communities" as nuclear structures of large organizational systems under conditions of global turbulence based on mathematical models using the Wiener integral and Wiener entropy.

Methods. A review of the literature, a method of mathematical modeling using the Wiener integral and Wiener entropy phenomenon are applied for preventive risk management in "smart communities" as nuclear structures of large organizational systems for various purposes under the influence of global turbulence factors.

Results. A general description of the problem of preventive incident risk management in "smart communities" as nuclear structures of organizational systems has been presented. The expediency of using the Wiener integral and Wiener entropy for analysis and preventive risk management in "smart communities" in conditions of systemic turbulence is substantiated. Mathematical models are proposed that provide various stages of preventive risk management for problematic situations and dangerous incidents in "smart communities" within large organizational systems based on the Wiener integral. In particular, it is a risk identification and assessment model based on the Wiener integral, an early detection and forecasting model, and a model for optimizing preventive risk management strategies. In addition, numerical algorithms and model validation are proposed, as well as algorithms for preventive risk management in "smart communities".

Conclusion. The fundamentals of the approach to preventive incident risk management in "smart communities" as nuclear structures of large organizational systems based on the Wiener integral and Wiener entropy have been developed.

1. Milanovic B. Global Inequality: A New Approach for the Age of Globalization. Belknap Press, An Imprint of Harvard University Press, 2016, 320 р.

2. Motter A. E., Lai Y.-C. Cascade-based attacks on complex networks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2002, vol. 66, no. 6, pt. 2. https://doi.org/10.1103/PhysRevE.66.065102.

3. Meadows D. Н., Randers J., Meadows D. L. The Limits to Growth: The 30-year Update. Earthscan, 2004, 362 р.

4. Demidenko E. S., Dergacheva E. A. Burzhuazno-tehnogennoe unichtozhenie biosfernoj zhizni i zemnogo shara: mezhdisciplinarnoe issledovanie. Bourgeois-man-made Destruction of Biospheric Life and the Globe: An Interdisciplinary Study. Moscow, 2023. 276 p. (In Russ.)

5. Voronov M. V., Davydovsky A.G. Bioinspired scenario analysis of the relationship between the COVID-19 epidemic and distance learning technologies. Modelirovanie i analiz dannyh [Data Modeling and Analysis], 2022, vol. 12, no. 4, рр. 25–35. https://doi.org/10.17759/mda.2022120402 (In Russ.).

6. Lenton T. M., Rockström J., Gaffney O., Rahmstorf S., Richardson K., …, Schellnhuber H. J. Climate tipping points – too risky to bet against. Nature, 2019, vol. 575, no. 7784, рр. 592–595. https://doi.org/10.1038/ d41586-019-03595-0.

7. Antonakaki D., Spiliotopoulos D., Samaras C., Pratikakis P., Ioannidis S., Fragopoulou P. Social media analysis during political turbulence. PLoS One, 2017, vol. 31, no. 12 (10). Available at: https://journals. plos.org/plosone/article?id=10.1371/journal.pone.0186836 (accessed 30.04.2026). https://doi.org/10.1371/journal.pone.0186836.

8. Schwab K., Davis N. Shaping the Future of the Fourth Industrial Revolution. Penguin group, 2018, 288 р.

9. Brisini K. S., Solomon D. H. Relational turbulence and social network engagement during the summer of COVID-19: A repeated measures, dyadic analysis. Journal of Social and Personal Relationships, 2022, vol. 39, no. 8, рр. 2435–2453. https://doi.org/10.1177/02654075221080760.

10. Nazaretyan A. P. Antropologija nasilija i kul'tura samoorganizacii: ocherki po jevoljucionnoistoricheskoj psihologii. Anthropology of Violence and Culture of Self-organization: Essays on Evolutionary and Historical Psychology. Moscow, LKI, 2007, 256 p. (In Russ.).

11. Helbing D. Globally networked risks and how to respond. Nature, 2013, vol. 497, рр. 51–59. https://doi.org/10.1038/nature12047.

12. Belkin G. L., Frolov M. I. (eds.). Humanity in the New Reality: Global Biotechnological Challenges. Moscow, Canon-Plus, 2022, 496 p. (In Russ.).

13. Kruglikov S. V., Davidovsky A. G. Modelling the risks of "smart city" development as a complex sociotechnical system. Informatika [Informatics], 2025, vol. 22, no. 2, pp. 7−32 (In Russ.). https://doi.org/10.37661/1816-0301-2025-22-2-7-32.

14. Wiener N. Nonlinear Problems in Random Theory. Literary Licensing, LLC, 2013, 140 р.

15. Davidovsky A. G., Kruglikov S. V. Modeling information exchange processes for synthesizing a business reference model of the executive committee of a city (region). Razvitie informatizacii i gosudarstvennoj sistemy nauchno-tehnicheskoj informacii (RINTI-2023): doklady XXII Mezhdunarodnoj nauchno-tehnicheskoj konferencii, Minsk, 16 nojabrja 2023 g. [Development of Informatization and the State System of Scientific and Technical Information (RINTI-2023): Reports of the XXII International Scientific and Technical Conference, Minsk, 16 November 2023]. Minsk, Ob'edinennyj institut problem informatiki Nacional'noj akademii nauk Belarusi, 2023, pp. 74–81 (In Russ.).

16. Davidovsky A. G. The problem of forecasting the digital transformation of enterprises and organizations. Sistemnoe modelirovanie social'no-jekonomicheskih processov: trudy 46-j Mezhdunarodnoj nauchnoj shkolyseminara, Ufa, 9–15 oktjabrja 2023 g. [System Modeling of Socio-economic Processes: Proceedings of the 46th International Scientific School-seminar, Ufa, 9–15 October 2023]. In I. N. Shchepina (ed.). Voronezh, Istoki, 2024, рp. 315–320 (In Russ.).

17. Kashchenko S. A. Dinamika modelei na osnove logisticheskogo uravneniya s zapazdyvaniem. Dynamics of Models Based on the Logistic Equation with Delay. Moscow, KRASAND, 2020, 576 p. (In Russ).

18. Antsev G. V., Gayenko V. P. Bezopasnost' iskusstvennyh sistem: upravlenie bezopasnost'ju i riskami. Tezaurus. Safety of Artificial Systems: Safety and Risk Management. Thesaurus. Moscow, Radiotechnika, 2022, 680 p. (In Russ.).

19. Korn G., Korn T. Sprovochnik po matematike dlya nauchnyh rabotnikov i inschenerov. Handbook of Mathematics for Scientists and Engineers. Moscow, Nauka, 1977, 831 p. (In Russ).

20. Dyachko A. G. Matematicheskoe i imitacionnoe modelirovanie proizvodstvennyh sistem. Mathematical and Simulation Modeling of Production Systems. Moscow, MISIS, 2007, 540 p. (In Russ).