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Information × Registration Number 0221U100570, 0120U104004 , R & D reports Title Complex dynamical systems in the sciences: theory, mathematical modelling, computing and application to advanced technology popup.stage_title Head Timokha Oleksandr M., Доктор фізико-математичних наук Registration Date 07-01-2021 Organization The Institute of Mathematics of NASU popup.description2 Object of study: Complex dynamical systems associated with with real applications and methods of mathematical modelling of floating tankers and neural networks. Project goal: Mathematical knowledge of complex dynamical systems and their solutions by synthesis of different types (in terms of differential equations, nonlinear / analytical mechanics and computational mathematics) of analytical and numerical approaches and methods, development on this basis the mathematical modelling for a number of current problems of the science, in particular, natural and artificial neural networks and design of marine and aerospace structures. Research methods: Methods of mathematical modeling, nonlinear adaptive modal methods which describe the resonant sloshing in containers, methods of invariant domains, stable cluster regimes, hierarchic structures, numerical experiment, schematic and bifurcation diagrams, histograms, phase portraits, bifurcation theory, perturbation theory, KAM theory, complexity and chaos theory, Lyapunov functions, asymptotic methods of nonlinear mechanics, inverted and pseudo-inverted operators, etc. Keywords: Complex dynamical systems, oscillator networks, bifurcation, symmetry, sloshing, impulse boundary value problem, integro-differential equations, exponential dichotomy. Product Description popup.authors Bondar Ivanna A Burylko Oleksandr A Vasylyk Vitalii B Lahodzinskyi Oleksandr Ye Lokaziuk Oleksandra V Pokutnyi Oleksander O Raynovskyy Ihor A Satur Oksana R Timokha Olexander M popup.nrat_date 2021-03-17 Close