Abstract
Based on an analysis of the experimental data obtained for various catastrophic phenomena, Malinetskii et al. [1] considered the main parameters of a process preceding the catastrophe and proposed the following function of time that describes this process: I(t) = A + B(t c − t)α[1 + Ccos(θ log(t c − t) − ϕ)]. The passage to complex quantities and substitution of variables reveal a power-law character of this approximation. Using this approach, differential equations determining the function that describes the precatastrophic behavior are obtained.
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References
G. G. Malinetskii, A. B. Potapov, and V. A. Vladimirov, Risk Management: Risk, Sustainable Development, Synergetics (Nauka, Moscow, 2000) [in Russian].
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M. A. Basin, in Proceedings of the International Intersubject Scientific Practical Conference on Modern Problems of Science and Education, Kerch, 2001, pp. 12–13.
M. A. Basin, Computers, Vortices, Resonances, Wave Theory of Structure-System Interaction (Norma, St. Petersburg, 2002), Chap. 2 [in Russian].
V. I. Arnold, Ordinary Differential Equations (Nauka, Moscow, 1984) [in Russian].
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Original Russian Text © M.A. Basin, 2006, published in Pis’ma v Zhurnal Tekhnicheskoĭ Fiziki, 2006, Vol. 32, No. 8, pp. 30–33.
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Basin, M.A. Differential equations determining the function that describes precatastrophic behavior of a system. Tech. Phys. Lett. 32, 338–339 (2006). https://doi.org/10.1134/S1063785006040195
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DOI: https://doi.org/10.1134/S1063785006040195