Analysis and forecast of the environmental radioactivity dynamics based on methods of chaos theory: general scheme and some application

A.V. Glushkov; E.R. Gubanova; O.Yu. Khetselius; G.P. Prepelitsa; A.A. Svinarenko; Yu.Ya. Bunyakova; V.V. Buyadzhi

doi:10.31481/uhmj.16.2015.05

A.V. Glushkov
E.R. Gubanova
O.Yu. Khetselius
G.P. Prepelitsa
A.A. Svinarenko
Yu.Ya. Bunyakova
V.V. Buyadzhi

DOI: https://doi.org/10.31481/uhmj.16.2015.05

Keywords: environmental radioactivity dynamics, the ecological state, time series of concentrations, pollutants, analysis and prediction methods of the theory of chaos

Abstract

We present firstly a new whole technique of analysis, processing and forecasting environmental radioactivity dynamics, which has been earlier developed for the atmospheric pollution dynamics analysis and investigation of chaotic feature sin dynamics of the typical hydroecological systems. The general formalism include: a) A general qualitative analysis of dynamical problem of the environmental radioactivity dynamics (including a qualitative analysis from the viewpoint of ordinary differential equations, the “Arnold-analysis”); b) checking for the presence of a chaotic (stochastic) features and regimes (the Gottwald-Melbourne’s test; the method of correlation dimension); c) Reducing the phase space (choice of the time delay, the definition of the embedding space by methods of correlation dimension algorithm and false nearest neighbor points); d) Determination of the dynamic invariants of a chaotic system (Computation of the global Lyapunov dimension λ_a; determination of the Kaplan-York dimension d_L and average limits of predictability Pr_max on the basis of the advanced algorithms; e) A non-linear prediction (forecasting) of an dynamical evolution of the system. The last block indeed includes new (in a theory of environmental radioactivity dynamics) methods and algorithms of nonlinear prediction such as methods of predicted trajectories, stochastic propagators and neural networks modelling, renorm-analysis with blocks of the polynomial approximations, wavelet-expansions etc.

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