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Information × Registration Number 0223U002856, 0118U003024 , R & D reports Title Process exploration of synchronization and management of c o l l e c t i f dynamic of neural system popup.stage_title Head Maystrenko Volodymyr L., Кандидат фізико-математичних наук Registration Date 13-03-2023 Organization National Academy of Sciences of Ukraine Technical center popup.description2  The object of research on the topic: mathematical models of complex nonlinear phenomena and processes in networks of coupled oscillators. The purpose of the work: the study of synchronization and chaotic dynamics for a wide range of nonlinear evolutionary processes in systems of coupled oscillators of various nature and the search for optimal modes of their operation when applied in neural networks. Research methods: qualitative and numerical analytical methods for the analysis of nonlinear mathematical models, the application of the theory of dynamic systems to study the synchronization and stability of solutions, the use of bifurcation theory to study the behavior of solutions depending on the parameters. New fundamental results from the mathematical modeling of nonlinear systems were obtained, in particular, the conditions of existence and stability of various types of solutions and their bifurcations were investigated. The main attention was paid to the study of mathematical regularities of the phenomenon of partial synchronization, i.e. so-called chimeric states, which play a key role in a wide range of problems in physics, chemistry, biology, medicine, and social sciences. The first section of the report examines the chimeric states in one-dimensional models and proposes methods for analyzing their properties and practical use. The second section is devoted to the study of spiral wave chimeric and solitary states in networks of oscillators with inertia using the example of the 2D (ie, two-dimensional) Kuramoto model. Their appearance from random initial conditions, their transformation as the radius and strength of connection increase are studied. KEYWORDS: chimeric states, networks of coupled oscillators, Kuramoto model, homoclinic and heteroclinic cycles, phase and frequency synchronization, bifurcations, nonlinear dynamical systems and chaos. Product Description popup.authors Dushek Iryna I Maistrenko Volodymyr L Maistrenko Iuriy L Osiv Oleksii P Salnikov Andrii O Slyusar Ievgen A Sudakov Oleksandr O Cheredarchuk Andrii I popup.nrat_date 2023-03-13 Close