Analysis and forecast of the hydroecological system pollution dynamics based on methods of chaos theory: New general scheme

Authors: A.V. Glushkov

Year: 2015

Issue: 19

Pages: 12-17


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 λα; 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


  1. Bunyakova Yu.Ya., Glushkov A.V. Analysis and forecast of the impact of anthropogenic factors on air basein of an industrial city. Odessa: Ecology, 2010.256p. (In Russian)
  2. Glushkov A.V., Khokhlov V.N., Serbov N.G., Bunyakova Yu.Ya., Balan A.K., Balanyuk E.P. Low-dimensional chaos in the time series of concentrations of pollutants in an atmosphere and hydrosphere. Vìsn. Odes. derž. ekol. unìv. – Bulletin of Odessa state environmental university, 2007, vol. 4, pp.337-348. (In Russian)
  3. Glushkov A.V. Analysis and forecast of the anthropogenic impact on industrial city’s atmosphere based on methods of chaos theory: new general scheme. Ukr. gìdrometeorol. ž. – Ukranian hydrometeorological journal, 2014, no. 15, pp. 32-36.
  4. Khokhlov V.N., Glushkov A.V., Loboda N.S., Bunyakova Yu.Ya. Short-range forecast of atmospheric pollutants using non-linear prediction method. Atmospheric Environment. The Netherlands: Elsevier, 2008, vol.42, pp.7284–7292.
  5. Glushkov A.V., Khokhlov V.N., Prepelitsa G.P., Tsenenko I.A. Temporal variability of the atmosphere ozone content: Effect of North-Atlantic oscillation. Optics of atmosphere and ocean, 2004, vol.14, no.7, pp.219-223.
  6. Glushkov A.V., Loboda N.S., Khokhlov V.N. Using meteorological data for reconstruction of annual runoff series over an ungauged area: Empirical orthogonal functions approach to Moldova-Southwest Ukraine region. Atmospheric Research. Elseiver, 2005 vol.77 pp.100-113.
  7. Glushkov A.V., Kuzakon’ V.M., Khetselius O.Yu., Bunyakova Yu.Ya., Zaichko P.A. Geometry of Chaos: Consistent combined approach to treating chaotic dynamics atmospheric pollutants and its forecasting. Proceedings of International Geometry Center, 2013, vol.6, no.3, pp.6-13.
  8. Glushkov A.V., Rusov V.N., Loboda N.S., Khetselius O.Yu., Khokhlov V.N., Svinarenko A.A., Prepelitsa G.P. On possible genesis of fractal dimensions in the turbulent pulsations of cosmic plasma – galactic-origin rays – turbulent pulsation in planetary atmosphere system. Adv. in Space Research. Elsevier, 2008, vol.42(9), pp.1614-1617.
  9. Glushkov A.V., Loboda N.S., Khokhlov V.N., Lovett L. Using non-decimated wavelet decomposition to analyse time variations of North Atlantic Oscillation, eddy kinetic energy, and Ukrainian precipitation. Journal of Hydrology. Elseiver, 2006, vol.322, no. 1-4, pp.14-24.
  10. Glushkov A.V., Khetselius O.Yu., Brusentseva S.V., Zaichko P.A., Ternovsky V.B. Adv. in Neural Networks, Fuzzy Systems and Artificial Intelligence. Series: Recent Adv. in Computer Engineering. Gdansk: WSEAS, 2014, vol.21, pp.69-75. (Ed.: J. Balicki).
  11. Glushkov A.V., Svinarenko A.A., Buyadzhi V.V., Zaichko P.A., Ternovsky V.B. Neural Networks, Fuzzy Systems and Artificial Intelligence, Series: Recent Adv. in Computer Engineering. Gdansk: WSEAS, 2014, vol.21, pp. 143-150 (Ed.: J. Balicki)
  12. Rusov V.D., Glushkov A.V., Vaschenko V.N., Myhalus O.T., Bondartchuk Yu.A. etal. Galactic cosmic rays – clouds effect and bifurcation model of the earth global climate. Part 1. Theory. Jour-nal of Atmospheric and Solar-Terrestrial Physics. Elsevier, 2010, vol.72, pp.498-508.
  13. Sivakumar B. Chaos theory in geophysics: past, present and future. Chaos, Solitons & Fractals, 2004, vol.19, №2, pp.441-462.
  14. Chelani A.B. Predicting chaotic time series of PM10 concentration using artificial neural network. Int. J. Environ. Stud, 2005, vol.62. №2, pp. 181-191.
  15. Gottwald G.A., Melbourne I. A new test for chaos in deterministic systems. Proc. Roy. Soc. London. Ser. A. Mathemat. Phys. Sci., 2004, vol.460, pp.603-611.
  16. Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S. Geometry from a time series. Phys. Rev. Lett., 1980, vol.45, pp.712-716.
  17. Kennel M., Brown R., Abarbanel H. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A., 1992, vol.45, pp.3403-3411.
  18. Abarbanel H.D.I., Brown R., Sidorowich J.J., Tsimring L.Sh. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys, 1993, vol.65, pp.1331-1392.
  19. Schreiber T. Interdisciplinary application of nonlinear time series methods. Phys. Rep., 1999, vol.308, pp.1-64.
  20. Fraser A.M., Swinney H. Independent coordinates for strange attractors from mutual information. Phys. Rev. A., 1986, vol.33, pp.1134-1140.
  21. Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D, 1983, vol.9, pp.189-208.
  22. Gallager R.G. Information theory and reliable communication. NY: Wiley, 1968. 608 p.
  23. Mañé R. On the dimensions of the compact invariant sets of certain non-linear maps. Dynamical systems and turbulence, Warwick 1980. Lecture Notes in Mathematics no.898. Berlin: Springer, 1981, pp.230-242. (Eds: D.A. Rand, L.S. Young).
  24. Takens F. Detecting strange attractors in turbulence. Dynamical systems and turbulence, Warwick 1980. Lecture Notes in Mathematics no.898. Berlin: Springer, 1981, pp.366-381. (Eds: D.A. Rand, L.S. Young).
  25. Prepelitsa G.P., Glushkov A.V., Lepikh Ya.I., Buyadzhi V.V., Ternovsky V.B., Zaichko P.A., Chaotic dynamics of non-linear processes in atomic and molecular systems in electromagnetic field and semiconductor and fiber laser devices: new approaches, uniformity and charm of chaos. Sensor Electronics and Microsystems Techn., 2014, vol.11, no.4, pp.43-57.
Download full text (PDF)