Registration Number
0225U003685,
(0123U100853)
, R & D reports
Title
Mathematical modeling of complex dynamic systems and processes relevant for state security
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Методи та алгоритми розв’язування складних проблем для динамічних систем, актуальних для безпеки держави
Head
Tymokha Oleksandr M., Доктор фізико-математичних наук
Registration Date
01-08-2025
Organization
Institute of Mathematics of the National Academy of Sciences of Ukraine
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The overall goal is the construction, machine learning and analytical study of mathematical models in the form of complex dynamic systems, which are necessary for a number of military and security problems during intervention, but do not allow the application of traditional methods of numerical solution.
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Research report: 174 p., 8 chapters, 8 tables, 22 figures, 1 appendix, 291 sources.
COMPLEX DYNAMIC SYSTEMS, CONTROL, MACHINE LEARNING, SITUATIONAL AWARENESS, MATHEMATICAL MODELS OF COMBAT, CONFLICT, ELECTRICAL NETWORKS AND FINANCIAL MARKET, STOCHASTIC FLOWS.
Research object: mathematical models in the form of complex dynamic systems that arise in military and security tasks.
Purpose of the work: construction, machine learning and analytical study of mathematical models in the form of complex dynamic systems that necessarily arise for a number of military and security problems during intervention, but do not allow the use of traditional numerical solution methods.
Research methods: numerical-analytic, asymptotic, spectral, variational, theories of differential equations, bifurcations, potential, etc.
Results and their novelty: new machine learning methods have been created, applicable to the problem of improving situational awareness; methods for synthesizing control systems for technical objects under conditions of uncertainty and exogenous disturbances have been developed; methods for calculating dynamic characteristics of missiles, mathematical models of the dynamics of power grids and the financial market, absorption and diffusion processes, filtration of gases and liquids, image processing have been constructed; methods for optimal control and classification of stochastic systems, etc. have been constructed. The results are fundamental in nature and make a significant contribution to the development of mathematical science.
Description of scientific publications: 30 works, among them — 23 articles / chapters of collective monographs.
Product Description
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Boichuk Oleksandr А.
Vasylyk Vitalii B.
Hutlianskyi Volodymyr Ya.
Dvornyk Anatolii V.
Dorohovtsev Andrii A.
Karataieva Tetiana V.
Konstantinov Oleksandr V.
Koshmanenko Volodymyr D.
Lukovskyi Ivan O.
Mazko Oleksii G.
Makarov Volodymyr L.
Niesmielova Olha V.
Panchuk Anastasiia A.
Pylypenko Andrii Yu.
Pokutnyi Oleksandr O.
Portenko Mykola I.
Rudenko Oleksii V.
Riabov Georgii V.
Ryazanov Volodymyr I.
Satur Oksana R.
Semenova Yevheniia V.
Skrypnik Ihor I.
Solodkyi Serhii H.
Solodun Oleksandr V.
Sushko Iryna M.
Teplinskyi Oleksii Yu.
Tymokha Oleksandr M.
Tkachenko Viktor I.
Trotsenko Yurii V.
Feruk Viktor A.
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2025-08-01
