Analysis of the fractal structures in wave processes

Authors: O.Yu. Khetselius, A.A. Svinarenko

Year: 2013

Issue: 16

Pages: 222-226


On the basis of wavelet analysis and multifractal formalism it has been carried out an analysis of fractal structures in the wave processes (capillary-gravitational ripple).

Tags: fractals structures; wave processes


  1. Zosimov V.V., Lyamshev L.M. Fractals in wave processes//Phys. Uspekhi.-1995.-Vol.38.- P.347-380.
  2. Mandelbrot B. Fractal geometry of nature.- M.: Mir, 2002.-656р.
  3. Schertzer D., Lovejoy S. Fractals: Physical Origin and Properites, Ed. Peitronero L.-N.-Y.: Plenum Press.-1990.-P.71-92.
  4. 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.
  5. Zaslavsky G.M. Stochasticity of dynamical systems.- Moscow: Nauka.-1998.
  6. Grassberger P., Procaccia I. Measuring the strangeness of strange attractors// Physica D.- 1983.-Vol.9.-P.189-208.
  7. Sivakumar B. Chaos theory in geophysics: past, present and future // Chaos, Solitons & Fractals.- 2004.-Vol.19.-P.441-462.
  8. Kaplan J.L., Yorke J.A. Chaotic behavior of multidimensional difference equations // Functional differential equations and approximations of fixed points. Springer Lecture Notes in Mathematics No.730 / H.-O. Peitgen, H.-O. Walter (Eds.).- Berlin: Springer, 1979.-P.204-227.
  9. Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S. Geometry from a time series// Phys. Rev. Lett.-1980.-Vol.45.-P.712-716.
  10. Schreiber T. Interdisciplinary application of nonlinear time series methods // Phys. Rep.- 1999.-Vol.308.-P. 1-64.
  11. Svinarenko A.A. Regular and chaotic dynamics of multi-oscillator dynamical systems // Photoelectronics.-2002.-Vol.11.-P.81-84.
  12. Daubechies I. Ten Lectures on Wavelets.- Philadelphia: SIAM, 1992.- 380p.
  13. Morlet J., Arens G., Fourgeau E. and Giard D. Wave propagation and sampling theory// Geophysics.-1982.-Vol.47.-p.203-236.
  14. Nason G., von Sachs R., Kroisand G. Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum // J.Royal Stat.Soc. -2000.-Vol.B62.-P.271-292.
  15. Glushkov A.V., Khokhlov V.N., Svinarenko A.A., Bunyakova Yu.Ya., Prepelitsa G.P. Wavelet analysis and sensing the total ozone content in the earth atmosphere: Mycros technology “Geomath”//Sensor Electr. and Microsys.Techn.-2005.-Vol.2, N3.-P.51-60.
  16. Glushkov A.V., Khokhlov V.N., Tsenenko I.A. Atmospheric teleconnection patterns: wavelet analysis// Nonlin. Geophys.-2004.-Vol.11,N3.-P.285-293.
  17. 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 (Elsevier). -2008.-Vol.42.-P. 7284–7292.
  18. 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 (Elsevier).-2006.-Vol. 322,N1-4.-P.14-24.
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