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Information × Registration Number 0120U104004, ( 0221U100570  0221U107124  0221U107125  0223U005385  ) R & D request Title Complex dynamical systems in the sciences: theory, mathematical modelling, computing and application to advanced technology Head Tymokha Oleksandr M., Доктор фізико-математичних наук Registration Date 25-09-2020 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description1 The main generic purpose is to get a new fundamental mathematical knowledge concerning complex dynamical systems (evolutionary boundary problems incl. with a free boundary, systems of nonlinear (integro) differential equations, equations with fractional derivatives, etc., which have not a unique solution) and their solutions by synthesising different (in view of differential equations, nonlinear/analytical mechanics and computational mathematics) analytical and computational approaches and methods and, based on that, to develop mathematical modelling of a series of actual problems of the sciences, e.g., for understanding the mass transport in a limited fluid volume, natural and artificial neural networks, adequate description of technological processes in bioreactors for the protein production, in acoustical levitators, for designing marine and aerospace constructions. The first scientific goal is to develop analytical and computational methods for studying stability, bifurcations of solutions, chaos, synchronization, etc. The authors collaborate with leading Ukrainian and international groups of physicists, engineers, biologists and specialists of the IT industry (neural networks), who use their mathematical results to improve mathematical models. Therefore, the second scientific goal is new methods of mathematical modelling based on machine learning from small data. The proposal is collected from coupled subprojects, which have their own specific goals, e.g., (a) description of synchronization, chaos and chimera structures, etc. in networks of coupled oscillators, (b) new mathematical theory of the Lagrangian mean, which clarifies the Prandtl phenomenon, (c) variational formalism for floating tankers and fish cages, (d) generalised theories of global bifurcations and solvability of evolutionary boundary value problems, (e) exponentially convergent algorithms (admit the parallelization) for equations with fractional derivatives and unbounded operator coefficients. popup.nrat_date 2024-12-10 Close