ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Koronovskii A. A., Minjuhin I. M., Tyshenko A. A., Hramov A. E., Midzjanovskaja I. S., Sitnikova E. Y. Application of continuous wavelet transform to analysis of intermittent behavior. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 4, pp. 34-54. DOI: 10.18500/0869-6632-2007-15-4-34-54

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
530.182(075.8)
DOI: 
10.18500/0869-6632-2007-15-4-34-54

Application of continuous wavelet transform to analysis of intermittent behavior

Autors: 
Koronovskii Aleksei Aleksandrovich, Saratov State University
Minjuhin Igor Mihajlovich, Saratov State University
Tyshenko Aleksandr Aleksandrovich, Saratov State University
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal University
Midzjanovskaja Inna Stanislavovna, Federal State Budgetary Institution of Science "Institute of Higher Nervous Activity and Neurophysiology RAS"
Sitnikova Evgenia Yurievna, Federal State Budgetary Institution of Science "Institute of Higher Nervous Activity and Neurophysiology RAS"
Abstract: 

Effective method of signals analysis based on the continuous wavelet transform is proposed in this paper. Application of this method to estimation of mean value both of laminar and turbulent phase durations corresponding to different types of intermittent behavior is considered including analysis of time series produced by living systems. It is shown that the proposed method is stable to noise and fluctuations distorting the initial time series.  

Key words: 
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Reference: 
  1. Berge P, Pomo I, Vidal C. Order in Chaos. Moscow: Mir; 1991. (in Russian).
  2. Manneville P, Pomeau Yv. Different ways to turbulence in dissipative dynamical systems. Physica D. 1980;1(2):219–226.
  3. Rosenblum MG, Pikovsky AS, Kurths J. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 1997;78(22):4193–4196. DOI: 10.1103/PhysRevLett.78.4193.
  4. Boccaletti S, Valladares DL. Characterization of intermittent lag synchronization. Phys. Rev. E. 2000;62(5):7497–7500. DOI: 10.1103/physreve.62.7497.
  5. Hramov AE, Koronovskii AA. Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators. Europhysics Letters. 2005;70(2):169–175. DOI: 10.1209/epl/i2004-10488-6.
  6. Koronovsky AA, Kuznetsova GD, Midzyanovskaya IS, Sitnikova EY, Trubetskov DI, Khramov AE. Patterns of intermittent behavior in spontaneous non-convulsive convulsive activity in rats. Doklady Akademii Nauk. 2006;409(2):274–276.
  7. Berge P, Pomeau Y, Vidal Ch. L’Ordre Dans Le Chaos; 1988.
  8. Dubois M, Rubio M, Berge P. Experimental evidence of intermittencies associated with a subharmonic bifurcation. Phys. Rev. Lett. 1983;51:1446–1449. DOI: 10.1103/PhysRevLett.51.1446.
  9. Platt N, Spiegel EA, Tresser C. On–off intermittency: a mechanism for bursting. Phys. Rev. Lett. 1993;70(3):279–282. DOI: 10.1103/PhysRevLett.70.279.
  10. Pikovsky A, Osipov G, Rosenblum M, Zaks M, Kurths J. Attractor–repeller collision and eyelet intermittency at the transition to phase synchronization. Phys. Rev. Lett. 1997;79(1):47–50. DOI: 10.1103/PhysRevLett.79.47.
  11. Zhan M, Wei GW, Lai CH. Transition from intermittency to periodicity in lag synchronization in coupled Rossler oscillators. Phys. Rev. E. 2002;65(3):036202. DOI: 10.1103/PhysRevE.65.036202.
  12. Koronovsky AA, Khramov AE. An effective wavelet analysis of the transition to chaos via intermittency. Technical Physics Letters. 2001;27(1):1–5. DOI: 10.1134/1.1345150.
  13. Koronovsky AA, Khramov AE. Continuous wavelet analysis and its applications. Moscow: Fizmatlit; 2003. (in Russian).
  14. Daubechies I. Ten lectures on wavelets. SIAM; 1992.
  15. Torresani B. Continuous wavelet transform. Paris: Savoire; 1995.
  16. Koronovskii AA, Tyshchenko AA, Hramov AE. Turbulent phase distribution during lag synchronization breakage. Tech. Phys. Lett. 2005;31:901–904. DOI: 10.1134/1.2136947.
  17. Hramov AE, Koronovskii AA. An approach to chaotic synchronization. Chaos. 2004;14(3):603–610. DOI: 10.1063/1.1775991.
  18. Schuster G. Deterministic Chaos. Moscow: Mir; 1988. (in Russian).
  19. Pecora LM, Carroll TL. Driving systems with chaotic signals. Phys. Rev. A. 1991;44(4):2374–2383. DOI: 10.1103/physreva.44.2374.
  20. Murali K, Lakshmanan M. Drive-response scenario of chaos synchronization in identical nonlinear systems. Phys. Rev. E. 1994;49(6):4882–4885. DOI: 10.1103/physreve.49.4882.
  21. Heagy JF, Platt N, Hammel SM. Characterization of on–off intermittency. Phys. Rev. E. 1994;49(2):1140–1150. DOI: 10.1103/physreve.49.1140.
  22. Koronovskii AA, Moskalenko OI, Khramov AE. New universality type in chaotic synchronization of dynamic systems. JETP Letters. 2004;80(1):20–22.
  23. Hramov AE, Koronovskii AA, Kurovskaya MK, Moskalenko OI. Synchronization of spectral components and its regularities in chaotic dynamical systems. Phys. Rev. E. 2005;71(5):056204. DOI: 10.1103/PhysRevE.71.056204.
  24. Press WH, Teukolsky SA, Vetterling WT, Flannery BT. Numerical Recipes. Cambridge: Cambridge University Press; 1997.
  25. Van Luijtelaar EL, Coenen AM. Two types of electrocortical paroxysms in an inbred strain of rats. Neurosci Lett. 1986;70(3):393–397. DOI: 10.1016/0304-3940(86)90586-0.
  26. Midzianovskaia IS. Two types of "spike-wave" discharges in the electrocorticogram of WAG/Rij rats, the genetic model of absence epilepsy. Zh. Vyssh. Nerv. Deyat. 1999;49(5):855–859.
  27. Luijtelaar EL, Coenen AM. Circadian rhythmicity in absence epilepsy in rats. Epilepsy Res. 1998;2(5):331–336. DOI: 10.1016/0920-1211(88)90042-3.
  28. Tass PA, Fieseler T, Dammers J, Dolan K, Morosan P, Majtanik M, Boers F, Muren A, Zilles K, Fink GR. Synchronization tomography: a method for three-dimensional localization of phase synchronized neuronal populations in the human brain using magnetoencephalography. Phys. Rev. Lett. 2003;90(8):088101. DOI: 10.1103/PhysRevLett.90.088101.
  29. Hramov AE, Koronovskii AA, Ponomarenko VI, Prokhorov MD. Detecting synchronization of self-sustained oscillators by external driving with varying frequency. Phys. Rev. E. 2006;73:026208. DOI: 10.1103/PhysRevE.73.026208.
  30. Koronovskii AA, Ponomarenko VI, Prokhorov MD, Hramov AE. The study of synchronization of self-oscillations on the universal data when changing the frequency of the external effects of using wavelet analysis. Technical Physics Letters. 2006; 32(11):81–88.
Received: 
20.03.2007
Accepted: 
07.06.2007
Published: 
31.07.2007
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