Search academic texts

Information × Registration Number 0223U005385, 0120U104004 , R & D reports Title Complex dynamical systems in the sciences: theory, mathematical modelling, computing and application to advanced technology popup.stage_title Head Tymokha Oleksandr M., Доктор фізико-математичних наук Registration Date 22-12-2023 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Report SRW: 347p., 11chapters, 38draw., 2tab., 405sour Research object: Complex dynamical systems in sciences. Purpose of work: Mathematical knowledge of complex dynamic systems that do not have a unique solution, and their solving through the synthesis of analytical and numerical approaches, development of mathematical modelling of current problems of science, in particular, neural networks, technological processes, design of structures. Research methods: mathematical modelling, bifurcation theory, asymptotic, functional, computational mathematics, etc. Results and novelty: first: a solution of the Sretensky problem accounting for nonlinearity and damping is given; methods of machine learning of fluid oscillation models are proposed; the existence criteria of solutions of boundary-value problems bounded on the entire axis under condition of exponential dichotomy on the semi-axes were obtained, problems with impulse influence were investigated, the theory of solvability and bifurcation conditions were constructed; an image of the solution of equations with fractional derivatives and unbounded operator coefficients was obtained, a numerical method was constructed with the possibility of parallelising calculations; a model was built with the adaptation of connections describing collective processes, their stability, bifurcations and multi-stability were studied; models of neural networks, iterative algorithms for finding solutions are built and chaotic conditions are described; separation of motions in boundary value problems in partial derivatives with a free surface is analysed. Implementation of the results of SRW: The project is of the theoretical character; it does not suggests creating scientific and technical products Description of the final product: A book is published, a collective monograph accepted by Springer Nature, 20 articles published, 10 submitted, 2 theses defended, 1 conference organised, talks at conferences- 30. Keywords: Complex dynamic systems Product Description popup.authors Bondar Ivanna Burylko Oleksandr А. Vasylyk Vitalii Lahodzinskyi Oleksandr Ye Lokaziuk Oleksandra Pokutnyi Oleksandr O. Raynovskyy Ihor A Satur Oksana R popup.nrat_date 2023-12-22 Close