Browsing by Author "Ignatenko, Anna"

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Analysis and forecast of the environmental radioactivity dynamics based on the methods of chaos theory: general conceptions
(Publishing House of Lviv Polytechnic National University, 2016) Glushkov, Alexander; Safranov, Timur; Khetselius, Olga; Ignatenko, Anna; Buyadzhi, Vasily; Svinarenko, Andrey
For the first time, we present a completely new technique of analysis, processing and forecasting of any time series of the environmental radioactivity dynamics, which schematically is as follows: a) general qualitative analysis of a dynamical problem, typical environmental radioactivity dynamics (including a qualitative analysis from the viewpoint of ordinary differential equations, the “Arnold-analysis”); b) checking for the presence of chaotic (stochastic) features and regimes (the Gottwald-Melbourne’s test; the correlation dimension method); c) reducing the phase space (the choice of time delay, the definition of the embedding space by the correlation dimension methods and false nearest neighbours algorithms); d) determination of the dynamic invariants of a chaotic system (computation of the global Lyapunov dimension la; determination of the Kaplan-Yorke dimension dL and average limits of predictability Prmax on the basis of the advanced algorithms; e) a nonlinear prediction (forecasting) of any dynamical system evolution. The last block really includes new (in the theory of environmental radioactivity dynamics and environmental protection) methods and algorithms of nonlinear prediction such as methods of predicted trajectories, stochastic propagators and neural networks modeling, renormanalysis with blocks of polynomial approximations, wavelet-expansions etc.
Modeling evolutionary dynamics of complex ecosystems using combined chaos theory and neural networks methods: I. Formal theoretical basis for application to environmental radioactivity dynamics
(Lviv Politechnic Publishing House, 2017-09-08) Glushkov, Alexander; Khetselius, Olga; Safranov, Tamerlan; Buyadzhi, Vasily; Ignatenko, Anna; Svinarenko, Andrey; Odessa State Environmental University
We present elements of the formal mathematical approach to the analysis, modeling and further prediction of the nonlinear dynamics of chaotic systems based on the methods of nonlinear analysis and neural networks. As the object of studing is the environmental radioactivity dynamics. Using such a combined method is proposed for the first time in the environmental radioactivity dynamnics studying. Use of the information about the phase space in the simulation of the evolution of the physical process in time can be considered as a major innovation in the modeling of chaotic processes in the complex systems. This concept can be achieved by constructing a parameterized nonlinear function F (x, a), which transform y (n) to y(n+1) = = F[y(n),a], and then use different criteria for determining the parameters a . Firstly to build the desired functions it is offered using the wavelet expansions. Further, since there is the notion of local neighborhoods, we can create a model of the process occurring in the neighborhood, at the neighborhood and by combining together these local models to construct a global non-linear model to describe most of the structure of the attractor.