Registration Number
0221U107124,
0120U104004
, R & D reports
Title
Complex dynamical systems in the sciences: theory, mathematical modelling, computing and application to advanced technology
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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
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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
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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.
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2022-03-09
