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Information × Registration Number 0222U003598, 0116U008186 , R & D reports Title Development of analytical and numerical methods for modelling and optimization of complex dynamical systems and their using in applied problems. popup.stage_title Head Shavarovsky Bogdan Z., Доктор фізико-математичних наукYadzhak Mykhailo Stepanovych, д.ф.-м.н. Registration Date 03-05-2022 Organization Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach of the National Academy of Sciences of Ukraine popup.description2 The object of study is nonlinear dynamical systems in applied problems of physics and biomechanics as well as complex network systems. The purpose of the work is constructing new nonlinear mathematical models of complex dynamical systems and development of modern analytical and numerical methods of their research with using of effective software and hardware. The methods of investigations are methods of topology, algebra, differential geometry; modeling dynamical systems, numerical methods for solving the problems of mathematical physics and the theory of parallel computing. The results and their novelty are the following. A simple proof of the theorem about coloring cards on non-orientable surfaces and a simple method for constructing the exponential number of orientable triangle embeddings of the order complete graph are proposed; the construction of graph coverings with preserving a cyclic connection, which allows to obtain new edge uncolorable cubic graphs, is elaborated; the theorem on the Dirac type reduction of bi-Poisson struc¬tures given on some smooth connected manifold is proven; the Lie-algebraic met¬hod for constructing the integrable nonlinear dynamical systems with space fractional derivatives is developed; the problem of solvability for certain types of matrix equations is investigated and some methods for constructing their solutions are proposed; the stability and convergence of projection methods for solving the first kind Fredholm integral equations in the cases of simple and double layer potentials are investigated; the mathematical models, methodology and algorithms for calculating the dynamic and energy characteristics of human gait with the passively/actively controlled exoskeleton are elaborated; effective parallel algorithms for solving the three-dimensional problem of digital filtering and some approa¬ches to optimization of calculations in solving algorithmically complex problems are proposed. The obtained results can be applied to deve Product Description popup.authors Hentosh Oksana Ye. Demydyuk Myroslav V Korzhik Vladimir P. Mykytiuk Ihor V Petrychkovych Vasyl M Polischuk Oleksandr Anatoliovych Fedorchuk Vasyl Maksymovych Shchedryk Volodymyr Volodymyr P popup.nrat_date 2022-05-03 Close