C&SA | Contents

Volume 61 >>> № 2 MARCH — APRIL 2025

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DOI 10.34229/KCA2522-9664.25.2.5

UDC 517.9

K.L. Atoyev¹, P.S. Knopov²

¹ V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

konstantin_atoyev@yahoo.com

² V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

knopov1@yahoo.com

MATHEMATICAL MODEL FOR RISK ASSESSMENT OF CRITICAL INFRASTRUCTURE

Abstract. Mathematical models have been developed to study the vulnerability of critical infrastructure (CI), which allow for the assessment of the probability of selecting a particular target for an attack on CI, the likelihood that the attack will be successful, and the extent of human and material losses from the attack on CI. Risk assessment is carried out using a six-sector Lorenz model with variable coefficients, which integrates uniformly described economic sectors into a single structure. Each sector is considered in terms of productivity levels, the number of jobs, and structural disruptions. The use of smooth function theory methods allows for the forecasting of crisis phenomena, the selection of strategies to ensure a given level of CI security, the study of the emergence of rapid, abrupt changes in CI, the ranking of various threat levels, and the identification of weak links that significantly impact the formation of instability and the deformation of the security space.

Keywords: Lorentz model, mathematical modeling, critical infrastructure, deterministic chaos, risk assessment.

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REFERENCES

1. The Critical Entities Resilience Directive (CER). https://www.critical-entities-resilience -directive.com .

2. Wilkinson A., Elani S., Eidinow E. Risk world scenarios. Journal of Risk Research. 2003. Vol. 6, Iss. 4–6. P. 297–334. https://doi.org/10.1080/ .

3. Renn O., Laubichler M., Lucas K., Krger W., Schanze J., Scholz R.W., Schweizer P.-J. Systemic risks from different perspectives. Risk Analysis. 2022. Vol. 42, N 9. P. 1902–1920. https://onlinelibrary.wiley.com/ .

4. Ermoliev Y., von Vinterfeldt D. Systemic risk and security management. In: Managing Safety of Heterogeneous Systems. Y. Ermoliev, M. Makovski, K. Marti (Eds.). LNE. Vol. 658. Heidelberg: Springer-Verlag, 2012. P. 19–49. https://doi.org/10.1007/ .

5. Norkin V.I., Gaivoronski A.A., Zaslavsky V.A., Knopov P.S. Models of the optimal resource allocation for the critical infrastructure protection. Cybernetics and Systems Analysis. 2018. Vol. 54, N 5. P. 696–706. https://doi.org/10.1007/ .

6. Pepelyaev V.A., Golodnikov A.N., Golodnikova N.A. Reliability optimization in plant production. Cybernetics and Systems Analysis. 2022. Vol. 58, N 1. P. 191–196. https://doi.org/10.1007/ .

7. Zgurovsky M. World transformation after the COVID-19 pandemic: The European context. In: Nexus of sustainability, studies in systems, decision and control. Zagorodny A., Bogdanov V., Zaporozhets A. (Eds.). Springer, 2024. Vol. 559. P. 165–183. https://doi.org/10.1007/ .

8. Atoyev K.L. The challenges to safety in the East Mediterranean: Mathematical modeling and risk management of marine ecosystems. Proc. NATO Advanced Study Institute on Strategic Management of Marine Ecosystems (1–11 October 2003, Nice, France). Nice, 2003. P. 179–197. http://dx.doi.org/10.1007/ .

9. Willis H.H., Morral A.R., Kelly T.K., Medby J.J. Estimating terrorism risk. Santa Monica, CA: Rand Corporation, 2005. 94 p. https://www.rand.org/ .

10. Kahnemann D., Tversky A. Subjective probability: a judgement of representativeness. Cognitive Psychology. 1972. Vol. 3, Iss. 3. P. 430–454. https://doi.org/10.1016/ .

11. Sergienko I.V., Yanenko V.M., Atoev K.L. A conceptual framework for managing the risk of ecological, technogenic, and sociogenic disasters. Cybernetics and Systems Analysis. 1997. Vol. 33, N 2. P. 203–219. https://doi.org/10.1007/ .

12. Atoyev K., Knopov P., Pepeliaev V., Kisaa P., Romaniuk R., Kalimoldayev M. The mathematical problems of complex systems investigation under uncertainties. In: Recent Advanced in Information Technology. Wojcik W., Sikora J. (Eds.). London: CRC Press, 2017. P. 135–171. https://doi.org/10.1201/ .

13. Atoyev K.L., Knopov P.S. Application of the robust methods for estimation of distribution parameters with a priori constraints on parameters in economics and engineering. Cybernetics and Systems Analysis. 2022. Vol. 58, N 5. P. 713–720. https://doi.org/10.1007/ .

14. Atoyev K.L., Knopov P.S. Mathematical modeling of climate change impact on relationships of economic sectors. Cybernetics and Systems Analysis. 2023. Vol. 59, N 4. P. 535–545. https://doi.org/10.1007/ .

15. Poston T., Stewart I. Catastrophe Theory and Its Applications [Russian translation]. Moscow: Mir, 1980. 607 p.

16. Chernavsky D.S. Synergetics and information: dynamic theory of information. Moscow: Nauka, 2001. 244 p.

17. Ebeling V., Engel-Herbert G. Extreme principles and catastrophe theory for stochastic models of nonlinear irreversible processes. Thermodynamics and kinetics of biological processes. Moscow: Nauka, 1980. P. 153–169.

18. Andronov A.A., Witt A.A., Khaikin S.E. Oscillation theory [in Russian]. Moscow: Fizmatgiz з, 1959. 916 p.

19. Atoyev K., Tomin A., Aksionova T. Global changes, new risks, and novel methods and tools of their assessment. Modeling and management of environmental security in Ukraine. In: Managing Critical Infrastructure Risks. NATO Science for Peace and Security Series C: Environmental Security. Linkov I., Wenning R.J., Kiker G.A. (Eds.). Dordrecht: Springer, 2007. P. 339–351. https://doi.org/10.1007/ .

20. Lorenz E. Deterministic nonperiodic flow. Journal of Atoms. Sci. 1963. Vol. 20. P. 130–141.

21. Krger W., Zio E. Vulnerable systems. London: Springer-Verlag, 2011. 204 p. https://doi.org/10.1007/ .

22. Zgurovsky M.Z., Pankratova N.D. System control of complex objects. In: System Analysis: Theory and Applications. Berlin; Heidelberg: Springer, 2007. P. 329–369. https://doi.org/ 10.1007/ .

23. Laszlo E. The age of bifurcation: Understanding the changing world. Gordon and Breach, 1991. 126 p.

24. Kaplan J.L., Yorke J.A. Preturbulence: A regime observed in a fluid flow model of Lorenz. Comm. Math. Phys. 1979. Vol. 67, Iss. 2. P. 93–108. https://doi.org/10.1007/ .

25. Magnitskii N.A., Sidorov S.V. New methods for chaotic dynamics. Singapore: World Scientific, 2006. 363 p.

26. Ermoliev Yu.M., Zagorodny A.G., Bogdanov V.I., Ermolieva T.Yu, Havlik P., Obersteiner M., Rovenskaya E. Linking distributed sectorial optimization models under asymmetric information: towards robust food-water-environmental nexus. In: FEW Nexux for Sustainable Development: Integrated Modeling & Robust Management. Ermoliev Yu., Zagorodny A., Bogdanov V., Ermolieva T., Kostyuchenko Yu. (Eds.). Kyiv: Akademperiodika, 2020. P. 303–322. https://www.calameo.com/ .

27. Pepelyaev V.A., Golodnikov A.N., Golodnikova N.A. Modeling the impact of climate change on the crop yield. Cybernetics and Systems Analysis. 2023. Vol. 59, N 6. P. 949–955. https://doi.org/10.1007/ .

28. Качинський А. Б. Безпека, загрози і ризик: наукові концепції та математичні методи. К.: ІПНБ, 2004. 472 с.

29. Shulzhenko S., Nechaieva T., Leshchenko I. The application of the optimal unit commitment problem for the studies of the national power sector development under system risks. In: Nexus of Sustainability, Studies in Systems, Decision and Control. Zagorodny A., Bogdanov V., Zaporozhets A. (Eds.). Springer, 2024. P. 147–164. https://doi.org/10.1007/ .

30. Pepelyaev V.A., Golodnikov A.N., Golodnikova N.A. Method of optimizing the structure of sowing areas for the adaptation of crop production to climate changes. Cybernetics and Systems Analysis. 2024. Vol. 60, N 3. P. 415–421. https://doi.org/10.1007/ .