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Published in: Automatic Control and Computer Sciences 8/2022

01-12-2022

Mathematical Model of the Spread of Computer Attacks on Critical Information Infrastructure

Authors: V. M. Krundyshev, M. O. Kalinin

Published in: Automatic Control and Computer Sciences | Issue 8/2022

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Abstract

This paper presents a mathematical model for the spread of computer attacks on critical information infrastructure based on the extension of the basic Lotka–Volterra model. Within the context of the proposed model, the problem is formulated, the point of stability of the system is determined, and a criterion is proposed for the adequacy of the attack detection methods to the changing parameters of the critical information infrastructure and existing cyber threats.
Literature
3.
go back to reference Zegzhda, D., Pavlenko, E., and Shtyrkina, A., Cybersecurity and control sustainability in digital economy and advanced production, The Economics of Digital Transformation, Devezas, T., Leitão, J., and Sarygulov, A., Eds., Studies on Entrepreneurship, Structural Change and Industrial Dynamics, Cham: Springer, 2021, pp. 173–185. https://doi.org/10.1007/978-3-030-59959-1_11 Zegzhda, D., Pavlenko, E., and Shtyrkina, A., Cybersecurity and control sustainability in digital economy and advanced production, The Economics of Digital Transformation, Devezas, T., Leitão, J., and Sarygulov, A., Eds., Studies on Entrepreneurship, Structural Change and Industrial Dynamics, Cham: Springer, 2021, pp. 173–185. https://​doi.​org/​10.​1007/​978-3-030-59959-1_​11
4.
go back to reference Ovasapyan, T., Moskvin, D., and Tsvetkov, A., Detection of attacks on the Internet of Things based on intelligent analysis of devices functioning indicators, 13th Int. Conf. on Security of Information and Networks, Merkez, Turkey, 2020, New York: Association for Computing Machinery, 2020, pp. 1–7. https://doi.org/10.1145/3433174.3433611 Ovasapyan, T., Moskvin, D., and Tsvetkov, A., Detection of attacks on the Internet of Things based on intelligent analysis of devices functioning indicators, 13th Int. Conf. on Security of Information and Networks, Merkez, Turkey, 2020, New York: Association for Computing Machinery, 2020, pp. 1–7.  https://​doi.​org/​10.​1145/​3433174.​3433611
7.
go back to reference Kolmogorov, A.N., Qualitative study of mathematical models of population dynamics, Probl. Kibern., 1972, vol. 25, no. 2, pp. 101–106.MathSciNet Kolmogorov, A.N., Qualitative study of mathematical models of population dynamics, Probl. Kibern., 1972, vol. 25, no. 2, pp. 101–106.MathSciNet
8.
go back to reference MacArtur, R., Graphical analysis of ecological systems, Some Mathematical Questions in Biology, Lectures on Mathematics in the Life Sciences, vol. 2, Providence, R.I.: The American Mathematical Society, 1970. MacArtur, R., Graphical analysis of ecological systems, Some Mathematical Questions in Biology, Lectures on Mathematics in the Life Sciences, vol. 2, Providence, R.I.: The American Mathematical Society, 1970.
9.
go back to reference Bazykin, A.D., Matematicheskaya biofizika vzaimodeistvuyushchikh populyatsii (Mathematical Biophysics of Interacting Populations), Moscow: Nauka, 1985. Bazykin, A.D., Matematicheskaya biofizika vzaimodeistvuyushchikh populyatsii (Mathematical Biophysics of Interacting Populations), Moscow: Nauka, 1985.
10.
go back to reference Titov, V.A. and Veinberg, R.R., Dynamic analysis of existing models based on Lotka–Volterra predator–prey equation, Fundam. Issled., 2016, no. 8-2, pp. 409–413. Titov, V.A. and Veinberg, R.R., Dynamic analysis of existing models based on Lotka–Volterra predator–prey equation, Fundam. Issled., 2016, no. 8-2, pp. 409–413.
11.
go back to reference Minaev, V.A., Sychev, M.P., Vaits, E.V., and Gracheva, Yu.V., Mathematical predator–prey model in information security system, Inf. Bezop., 2016, vol. 19, no. 3, pp. 397–400. Minaev, V.A., Sychev, M.P., Vaits, E.V., and Gracheva, Yu.V., Mathematical predator–prey model in information security system, Inf. Bezop., 2016, vol. 19, no. 3, pp. 397–400.
12.
go back to reference Bratus’, A.S., Novozhilov, A.S., and Platonov, A.P., Dinamicheskie sistemy i modeli biologii (Dynamic Systems and Models of Biology), Moscow: Fizmatlit, 2011. Bratus’, A.S., Novozhilov, A.S., and Platonov, A.P., Dinamicheskie sistemy i modeli biologii (Dynamic Systems and Models of Biology), Moscow: Fizmatlit, 2011.
13.
go back to reference Poincaré, A., Izbrannye trudy (Selected Works), Moscow: Nauka, 1972, vol. 2. Poincaré, A., Izbrannye trudy (Selected Works), Moscow: Nauka, 1972, vol. 2.
14.
go back to reference Romanov, M.F. and Fedorov, M.P., Matematicheskie modeli v ekologii. Uchebnoe posobie (Mathematical Models in Ecology: Textbook), St. Petersburg, Ivan Fedorov, 2003, 2nd ed. Romanov, M.F. and Fedorov, M.P., Matematicheskie modeli v ekologii. Uchebnoe posobie (Mathematical Models in Ecology: Textbook), St. Petersburg, Ivan Fedorov, 2003, 2nd ed.
15.
go back to reference Volterra, V., Leçons sur la théorie mathématique de la lutte pour la vie, Paris: Gauthier-Villars, 1931.MATH Volterra, V., Leçons sur la théorie mathématique de la lutte pour la vie, Paris: Gauthier-Villars, 1931.MATH
16.
go back to reference Dolinskii, A., Draganov, B., and Kozirskii, V., Nonequilibrium state of engineering systems, ECONTECHMOD, 2012, vol. 1, no. 1, pp. 33–34. Dolinskii, A., Draganov, B., and Kozirskii, V., Nonequilibrium state of engineering systems, ECONTECHMOD, 2012, vol. 1, no. 1, pp. 33–34.
18.
go back to reference Brauer, F., and Castillo-Chavez, C., Mathematical Models in Population Biology and Epidemiology, Heidelberg: Springer, 2000.MATH Brauer, F., and Castillo-Chavez, C., Mathematical Models in Population Biology and Epidemiology, Heidelberg: Springer, 2000.MATH
Metadata
Title
Mathematical Model of the Spread of Computer Attacks on Critical Information Infrastructure
Authors
V. M. Krundyshev
M. O. Kalinin
Publication date
01-12-2022
Publisher
Pleiades Publishing
Published in
Automatic Control and Computer Sciences / Issue 8/2022
Print ISSN: 0146-4116
Electronic ISSN: 1558-108X
DOI
https://doi.org/10.3103/S0146411622080089

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