Low-Dimenssional chaos in temporary raws of concentrations of pollution substances in atmosphere and hydrosphere

Authors: Glushkov, А.V., V.N. Khokhlov, N.G. Serbov, А.К. Balan, Yu.Ya.Bunyakova, and Е.P. Balanyuk

Year: 2007

Issue: 04

Pages: 337-348


It is studied dynamics of temporary rows of pollution concentrations in atmosphere and hydrosphere (on example of oxide of nitrogen and sulphury angydride in Gdan’sk atmosphere and chloric hydrocarbons in mouth zone of Danube r. and north-west part of Black sea) and discovered the low-dimenssional chaos.

Tags: dynamics of temporary rows of concentrations of the pollution substances; low-dimenssional chaos


  1. Smale S. Diffeomorphisms with many periodic points // Differential and combinatorial topology/ S.S. Cairns (ed.). Princeton: Princeton University Press, 1963.- P. 63-80.
  2. Wiggins S. Introduction to nonlinear dynamical systems and chaos. N.-Y.: Springer, 1997.- 688 p.
  3. Lorenz E.N. Deterministic nonperiodic flow// J.Atmos.Sci.-1963.-V.20, № 2.- P. 130-141.
  4. Tsonis A.A. Chaos: from theory to application. New York: Plenum Press, 1992.- 274 p.
  5. Ott E. Chaos in dynamical systems. Cambridge: Cambridge Univ. Press, 2002.-490 p.
  6. Letellier C., Aziz-Alaoui M.A. Analysis of the dynamics of a realistic ecological model // Chaos, Solitons & Fractals.- 2002.- V. 13, №1. – P.95-107.
  7. Sprott J.C., Vano J.A., Wildenberg J.C., Anderson M.B., Noel J.K. Coexistence and chaos in complex ecologies // Phys. Lett. A. -2005.- V. 335,№ 2-3.- P.207-212.
  8. Lanfredi M., Machhiato M. Searching for low dimensionality in air pollution time series // Europhys. Lett. – 1997.-V. 40. № 6.- P.589-594.
  9. Paluš M., Pelikán E., Eben K., Krejčíř P., Juruš P. Nonlinearity and prediction of air pollution // Artificial neural nets and genetic algorithms / V. Kurkova, N.C. Steele, R. Neruda, M. Karny (Eds.). Wien: Springer, 2001. – P.473-476.
  10. Chelani A.B. Predicting chaotic time series of PM10 concentration using artificial neural network // Int. J. Environ. Stud. 2005. – V.62, №2.- P. 181-191.
  11. Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S. Geometry from a time series // Phys. Rev. Lett.- 1980.-Vol. 45,№ 9.- P. 712-716.
  12. 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.- V. 65,№ 4.- P.1331-1392.
  13. Dynamical systems and turbulence, Warwick 1980. Lecture Notes in Mathematics No. 898 / D.A. Rand, L.S. Young (Eds.). Berlin: Springer-Verlag, 1981.- 390 p.
  14. Gallager R.G. Information theory and reliable communication. N.-Y/:Wiley, 1968.- 608p.
  15. Fraser A.M., Swinney H.L. Independent coordinates for strange attractors from mutual information // Phys. Rev. A.- 1986. – V. 33, №2. -P. 1134-1140.
  16. Schreiber T. Interdisciplinary application of nonlinear time series methods // Phys. Rep. 1999.- V.308,№ 1.- P. 1-64.
  17. Grassberger P, Procaccia I. Measuring the strangeness of strange attractors // Physica D.- 1983.- V. 9, № 1-2.- P. 189-208.
  18. Kennel M.B., Brown R., Abarbanel H.,Determining embedding dimension for phase-space reconstruction using geometry construction // Phys.Rev.A.-1992.-V.45.-P.3403-3411.
  19. Havstad J.W., Ehlers C.L. Attractor dimension of nonstationary dynamical systems from small data sets // Phys. Rev. A. – 1989. – V.39, № 2.- P. 845-853.
  20. Holzfuss J., Mayer-Kress G. An approach to error-estimation in application of dimension algo-rithms // Dimensions in chaotic systems / G. Mayer-Kress (ed.). N.-Y: Springer, 1986. -P.114-122.
  21. Tsonis A.A., Elsner J.B. The weather attractor over very short timescale // Nature.-1988.- V. 333,№ 6173.- P.545-547.
  22. Schuster H.G. Deterministic chaos: an introduction. New York: Wiley, 2005.- 312 p.
  23. Islam M.N., Sivakumar B. Characterization and prediction of runoff dynamics: a nonlinear dynamical view // Adv. Water Res. -2002.-V.25, № 2.- P.179-190.
  24. Хохлов В.Н. Хаос и предсказуемость концентраций парниковых газов в атмосфере // Вестник ОГЭКУ. -2005.- Вып.1.- С.11-19.
  25. Глушков А.В., Хохлов В.Н., Препелица Г., Цененко И., Временная изменчивость содержания метана: влияние североатлантической осцилляции//Опт.атм.и океана. -2004.-Т.17.-С.573-575
  26. Glushkov A.V., Khokhlov V.N., Tsenenko I.A., Atmospheric teleconnection patterns and eddy kinetic energy content: wavelet analysis// Nonlin. Proc. in Geophys.-2004.-V.11,N3.-P.285-293.
  27. Глушков А.В.,Сафранов Т.А.,Баланюк Е., О размерности аттрактора уравнений гидродинамической модели прибрежной циркуляции// Мет., климат., гидр. -2004.-№48.-С.308-312.
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