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Information × Registration Number 0221U107124, 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 27-12-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Research object: Exponentially convergent methods for problems with fractional derivatives. Complex dynamic models with adaptation. Purpose of work: Investigate the solutions of differential equations with fractional derivatives and unbounded operator coefficients in Banach spaces, construct a numerical exponential converging method admitting a parallelization of calculations, apply the numerical methods to diffusion problems in porous media. Construct a new oscillatory and neural models with adaptation and plasticity, to study the coexistence of conservative and dissipative dynamics in systems with time-reversible symmetry. Research methods: Methods of bifurcation theory, computational mathematics, etc. Results and novelty: first: – a solution image for differential equations with fractional derivatives and unbounded operator coefficients in Banach space is derived, a numerical method with allowing for parallelization of computation and establishment of estimates of convergence rate is constructed; – a model with adaptation of connections describing collective neural and economic processes is constructed, collective regimes, their stability, bifurcations and multistability are studied, multidimensional heteroclinic barrier structures in conservative-dissipative systems are examined, invariant sets of oscillators are described. Implementation of the results of SRW: The project is of the theoretical character; it does not suggests creating scientific and technical products. Keywords: Chaos, bifurcations, chimeric state, exponentially convergent method, parallelization. Product Description popup.authors Bondar Ivanna A Burylko Oleksandr A Vasylyk Vitalii Bogdanovych Lahodzinskyi Oleksandr Ye Lokaziuk Oleksandra V Pokutnyi Oleksander O Raynovskyy Ihor A Satur Oksana R Timokha Oleksandr M. popup.nrat_date 2022-03-09 Close