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Information × Registration Number 0225U003771, (0122U001693) , R & D reports Title Chaotic states in modulated systems popup.stage_title Хаотичні стани в модульованих системах Head Sveleba Serhii A., Доктор фізико-математичних наук Registration Date 15-08-2025 Organization Ivan Franko National University of Lviv popup.description1 The aim of the project is to find dimensional effects, pinning effects of incommensurate superstructure in the field of deformation of the main structure; construction of the theory of spatial dynamics of incommensurate superstructure in its various modes; construction of exact equations of amplitude and phase function of superstructure; establishment of dependences of behaviour of amplitude and phase function on symmetry of thermodynamic potential; determination of the contribution of harmonics of a incommensurate superstructure to its anisotropic interaction; study of the influence of surface energy on the dynamics of harmonics of incommensurate modulation waves. Investigate the dependence of learning error on the value of learning speed and sampling for multilayer neural networks. Applying the logistic function to the dependence of the learning error function of a multilayer neural network on the value of the learning speed and using the diagrams of branches and Fourier spectra to analyse the chaotic states in these systems. Calculations of chaotic states in other complex systems. popup.description2  The project studied new effects in the physics of disproportionately modulated systems due to their chaotic state. For the first time, the Adams method was applied to determine the dynamics of the superstructure depending on the anisotropic interaction, which is described by the Dzyaloshynskii invariant. The method of phenomenological description of superstructures was generalized to the case of periodic potential with complex spatial periodicity. The study of the dynamic modes of the superstructure from the symmetry of the thermodynamic potential and the values of the first integral of motion was carried out. A methodology for the study of maps of dynamic modes has been developed, and a study of maps of dynamic modes of non-interchangeable superstructures whose appearance is described by the Livshitsa invariant has been carried out. The Lyapunov method for determining the stability of NS systems was generalized to the case of ferroelectric and ferroelectric nature of spatial modulation and to other systems. The influence of surface energy on NS-modulated systems, as well as on harmonics of the phase function, was investigated. The maps of the dynamic regimes of the NS of the superstructure in the field of the spatially deformed structure were studied. The project solves a fundamental problem of chaos theory - violation of the stability of the NS superstructure as a sequence of an infinite number of stable commensurate states forming the "devil's ladder". A consistent theory of the dynamics of the NS of the superstructure during its genesis and in the sinusoidal, soliton, and stochastic regimes during interaction with defects and impurities is constructed. The thermodynamics of the NS of the superstructure in electric and mechanical fields and in the field of surface energy was studied. Amplitude and phase functions of the NS of the superstructure were obtained and the frequency spectrum of its harmonics was determined. Product Description popup.authors Velhosh Serhii R. Karbovnyk Ivan D. Katerynchuk Ivan M. Kashuba Andrii I. Kunyo Ivan M. Kushnir Oleh S. Luchechko Andrii P. Stahura Volodymyr B popup.nrat_date 2025-08-15 Close