Modeling evolutionary dynamics of complex ecosystems using combined chaos theory and neural networks methods: I. Formal theoretical basis for application to environmental radioactivity dynamics - Glushkov, Alexander; Khetselius, Olga; Safranov, Tamerlan; Buyadzhi, Vasily; Ignatenko, Anna; Svinarenko, Andrey (Lviv Politechnic Publishing House, 2017)
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.
Keywords: environmental radioactivity dynamics; the ecological state; time series of concentrations; pollutants; analysis and prediction methods of the theory of chaos