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 λa; determination of the Kaplan-York dimension dL and average limits of predictability Prmax 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.
Determination of the correlation dimension of an attractor in a pipe based on the theory of stochastic equations and equivalence of measures
