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Information × Registration Number 0214U000077, 0112U000026 , R & D reports Title Development of mathematical models and analysis methods for dynamical systems with applications to problems of constructing new information technologies popup.stage_title Head Kovalev Alexander Mikhaylovich, Skobelev Vladimir Gennadievich, Registration Date 15-01-2014 Organization Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine popup.description2 Object of investigation: dynanical systems presented either via systems of differential equations, or via equiations over finite algebraic structures. Aim of research: development of methods for investigation of stability for continuous dynamicla systems, synchronization for system of the synchronization systems of transmitter-receiver type with incomplete information, and development of methods for analysis of discrete dynamical systems represented by equations over algebraic structures. Methods of investigation: methods of Lyapunov's functions theory, methods of automata theory, methods of theory of algebraic systems, metods of algebraic geometry and methods for solving partially inversible problems of mechanics. Results and novelty: Solver, designed to test satistisfiability of linear arithmetic formulae over any finite associative ring with nonzero multiplication, is constructed and its time complexity is investigated. Set of quantum finite automata with input operators that commute is investigated. For continuous systems, the method of additional functions is generalized for nonautonomous case. The method for the synthesis of invariant relations, that are associated with dynamical systems composed by same transmitter and receiver, is developed to avoid the uncertainties of existing relations, that provide asymptotic estimation for the trajectory of transmitter with the values of the output function. Product Description popup.authors Астахова Тетяна Миколаївна Неспірний Віталій Миколайович Сапунов Сергій Валерійович Скобелєв Володимир Володимирович Щербак Володимир Федорович popup.nrat_date 2020-04-02 Close