**Authors: **A.V. Glushkov

**Year: **2015

**Issue: **19

**Pages: **12-17

**Abstract**

We present firstly a new whole technique of analysis, processing and forecasting any time series of the chemical pollutants in the typical hydroecological systems , which is schematically looked as follows: a). A general qualitative analysis of dynamical problem of the typical hydroecological systems (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

_{α}; 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 hydroecological systems and environmental protection) 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.

**Tags: **analysis and prediction methods of the theory of chaos; hydroecological systems; pollutants; the ecological state; time series of concentrations

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