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Multiresolution wavelet analysis of transients: numerical simulations and application to EEG

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Abstract

We explore the capabilities of multiresolution wavelet analysis (MWA) to characterize complex dynamics based on short data sets that can be applied for diagnosing inter-state transitions. Using the example of chaos–hyperchaos transitions in the model of two interacting Rössler systems, we establish the minimum amount of data necessary for reliable separation of chaotic and hyperchaotic oscillations and discuss how this amount changes depending on the length of the transient process. We then discuss transitions between wakefulness and artificial sleep in mice and estimate the duration of electroencephalograms (EEG) that provide separation between these states.

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References

  1. J.S. Bendat, A.G. Piersol, Random Data: Analysis and Measurement Procedures, 4th edn. (Wiley, Boca Raton, 2010)

    Book  MATH  Google Scholar 

  2. A.V. Oppenheim, G.C. Verghese, Signals, Systems and Inference (Pearson, India, 2015)

    Google Scholar 

  3. D.G. Manolakis, J.G. Proakis, Digital Signal Processing, 4th edn. (Pearson, India, 2006)

    Google Scholar 

  4. I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, Philadelphia, 1992)

    Book  MATH  Google Scholar 

  5. Y. Meyer, Wavelets: Algorithms & Applications (Society for Industrial and Applied Mathematics, Philadelphia, 1993)

    MATH  Google Scholar 

  6. B.B. Hubbard, The World According to Wavelets: The Story of a Mathematical Technique in the Making, 2nd edn. (CRC Press, Boca Raton, 1998)

    Book  MATH  Google Scholar 

  7. S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 3rd edn. (Academic Press, Cambridge, 2008)

    MATH  Google Scholar 

  8. P.S. Addison, The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance, 2nd edn. (CRC Press, Boca Raton, 2017)

    Book  MATH  Google Scholar 

  9. J.F. Muzy, E. Bacry, A. Arneodo, Phys. Rev. Lett. 67, 3515 (1991)

    Article  ADS  Google Scholar 

  10. A.E. Hramov, A.A. Koronovskii, V.A. Makarov, V.A. Maksimenko, A.N. Pavlov, E. Sitnikova, Wavelets in Neuroscience, 2nd edn. (Springer, Cham, 2021)

    Book  MATH  Google Scholar 

  11. N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung, H.H. Liu, Proceedings of the Royal Society of London A 454, 903 (1998)

    Article  ADS  Google Scholar 

  12. N.E. Huang, S.S.P. Shen, Hilbert–Huang Transform and its Applications (World Scientific, New Jersey, 1995)

    MATH  Google Scholar 

  13. C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger, Phys. Rev. E 49, 1685 (1994)

    Article  ADS  Google Scholar 

  14. C.-K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, Chaos 5, 82 (1995)

    Article  ADS  Google Scholar 

  15. R.M. Bryce, K.B. Sprague, Sci. Rep. 2, 315 (2012)

    Article  ADS  Google Scholar 

  16. Y.H. Shao, G.F. Gu, Z.Q. Jiang, W.X. Zhou, D. Sornette, Sci. Rep. 2, 835 (2012)

    Article  Google Scholar 

  17. N.S. Frolov, V.V. Grubov, V.A. Maksimenko, A. Lüttjohann, V.V. Makarov, A.N. Pavlov, E. Sitnikova, A.N. Pisarchik, J. Kurths, A.E. Hramov, Sci. Rep. 9, 7243 (2019)

    Article  ADS  Google Scholar 

  18. S. Thurner, M.C. Feurstein, M.C. Teich, Phys. Rev. Lett. 80, 1544 (1998)

    Article  ADS  Google Scholar 

  19. I.M. Dremin, V.I. Furletov, O.V. Ivanov, V.A. Nechitailo, V.G. Terziev, Control Eng. Practice 10, 599 (2002)

    Article  Google Scholar 

  20. A.N. Pavlov, O.N. Pavlova, O.V. Semyachkina-Glushkovskaya, J. Kurths, Chaos 31, 043110 (2021)

    Article  ADS  Google Scholar 

  21. G.A. Guyo, A.N. Pavlov, E.N. Pitsik, N.S. Frolov, A.A. Badarin, V.V. Grubov, O.N. Pavlova, A.E. Hramov, Chaos Solitons Fract. 158, 112038 (2022)

  22. A.N. Pavlov, O.N. Pavlova, Chaos Solitons Fract. 146, 110924 (2021)

  23. G. Strang, T. Nguyen, Wavelets and Filter Banks, 2nd edn. (Wellesley-Cambridge Press, Cambridge, 1996)

    MATH  Google Scholar 

  24. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, 3rd edn. (Cambridge University Press, Cambridge, 2007)

    MATH  Google Scholar 

  25. A.N. Akansu, R.A. Haddad, Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets, 2nd edn. (Academic Press, USA, 2001)

    MATH  Google Scholar 

  26. J.P. Muszkats, S.A. Seminara, M.I. Troparevsky (eds.), Applications of Wavelet Multiresolution Analysis (Springer, Cham, 2020)

    Google Scholar 

  27. O.N. Pavlova, G.A. Guyo, A.N. Pavlov, Physica A 585, 126406 (2022)

    Article  Google Scholar 

  28. D.E. Postnov, T.E. Vadivasova, O.V. Sosnovtseva, A.G. Balanov, V.S. Anishchenko, E. Mosekilde, Chaos 9, 227 (1999)

    Article  ADS  Google Scholar 

  29. A.N. Pavlov, O.V. Sosnovtseva, E. Mosekilde, Chaos Solitons Fract. 16, 801 (2003)

  30. P.L. Nunez, R. Srinivasan, Electric Fields of the Brain: The Neurophysics of EEG, 2nd edn. (Oxford University Press, Oxford, 2005)

    Google Scholar 

  31. J.C. Henry, Neurology 67, 2092 (2006)

    Article  Google Scholar 

  32. N.P. Castellanos, V.A. Makarov, J. Neurosci. Methods 158, 300 (2006)

    Article  Google Scholar 

  33. A.N. Pavlov, O.N. Pavlova, Y.K. Mohammad, J. Kurths, Phys. Rev. E 91, 022921 (2015)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the Russian Science Foundation (Agreement 19-12-00037) in the part of the theoretical and numerical studies. Physiological experiments described in Sects. 2.3 and 3.2 were carried out within the framework of the grant from the Government of the Russian Federation No. 075-15-2022-1094.

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Authors and Affiliations

  1. Saratov State University, Astrakhanskaya Str. 83, Saratov, 410012, Russia

    G. A. Guyo, O. N. Pavlova, I. A. Blokhina, O. V. Semyachkina-Glushkovskaya & A. N. Pavlov

  2. Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies”, Saratov, 410012, Russia

    G. A. Guyo & A. N. Pavlov

Authors
  1. G. A. Guyo
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  2. O. N. Pavlova
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  3. I. A. Blokhina
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  4. O. V. Semyachkina-Glushkovskaya
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  5. A. N. Pavlov
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Correspondence to A. N. Pavlov.

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Guyo, G.A., Pavlova, O.N., Blokhina, I.A. et al. Multiresolution wavelet analysis of transients: numerical simulations and application to EEG. Eur. Phys. J. Spec. Top. 232, 635–641 (2023). https://doi.org/10.1140/epjs/s11734-022-00710-7

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  • DOI: https://doi.org/10.1140/epjs/s11734-022-00710-7

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