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Information × Registration Number 0220U103197, 0118U004130 , R & D reports Title Physical processes in nonlinear systems of different nature popup.stage_title Head Vitrenko Andrii M., Кандидат фізико-математичних наук Registration Date 03-09-2020 Organization Sumy State University popup.description2  The object of research is processes in dynamical systems with regular, chaotic, and stochastic behavior. The aim of work is to investigate transitions induced by cross-correlated Gaussian white noises by methods of the mathematical theory of catastrophes, to develop virtual stands for demonstration of different types of behavior of dynamical systems by method of computer simulation. It is shown from general considerations that transitions induced by noises from unimodal (with one maximum) to bimodal (with two maxima) probability distribution of the system state can be qualitatively described by the normal form of the pitchfork bifurcation perturbed by one additive Gaussian white noise. A concrete example of the dynamical system is considered, and illustrations are given. To date, no warnings have been found regarding the description of processes in nature by the model that was once introduced for mathematical reasons. Virtual stands have been developed in LabVIEW to demonstrate chaotic behavior for a one-dimensional mapping with nonlinearity of the Gaussian function type multiplied by its argument describing the signals of an electronic autogenerator with delay, stochastic behavior for Wiener and Ornstein-Uhlenbeck processes describing the Brownian motion and noise-induced transitions in the genetic model, regular behavior for a series oscillating circuit. Virtual stands are science-based and can be implemented as e-learning tools, especially in blended and distance learning Product Description popup.authors Kruhliak Maksym V Makarenko Kostiantyn V Myronov Yevhenii M popup.nrat_date 2020-10-01 Close