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Information × Registration Number 0224U001409, 0119U002100 , R & D reports Title New generalized mathematical models with discrete time: cellular automata, neural networks, discrete equations and their possible applications. popup.stage_title Head Makarenko Olexandr S., Доктор фізико-математичних наук Registration Date 22-01-2024 Organization Educational and Scientific Complex "Institute for Applied System Analysis" of National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" popup.description2  Obtained estimates of fractal dimensions of attractors. Multivalued solutions of the logistic equation with anticipation and the issue of the complexity of their calculation are studied. Formal aspects of uncertainties related to the absence of classical stochastic laws are considered. Significant new results were obtained in the field of cellular automata. First, it was possible to formulate ways of generalizing cellular automata for use in the theory of computation in the case when the corresponding objects are multi-valued. A new type of cellular automata was also invented, which made it possible to use a partial type of ambiguity associated with the use of analytic functions. Also, new types of artificial neural networks have been proposed, allowing different types of ambiguity, in particular with branching. A generalization of ordinary single-valued artificial neural networks in the form of multi-valued networks, which can have several values ​​of elements and multi-valued connections between elements, is proposed. Modified Hopfield neural networks with the property of strong prediction are considered. Branching networks are described. New aspects of learning processes and possible areas of application of multi-valued neural networks were studied. New classes of problems described by models with advance (anticipation), as well as with the internal structure of elements, were studied. An analysis of the existing sources of uncertainty and the possibilities of their formalization, in particular those related to ambiguity, was carried out. One such environment for research is cellular automata. In the research, a description of analogues of the double-slit experiment for cellular automata is considered. The results of computer experiments are given. Some interpretations are proposed, including the distribution of state frequencies during evolution. The probable role of strong anticipation in such experiments is also described. Product Description popup.authors MAKARENKO OLEKSANDR SERGIYOVYCH Osaulenko Viacheslav M. Samorodov Eugene Lvovich Statkevich Vitaliy M. popup.nrat_date 2024-01-22 Close