ANALYSIS OF MULTIFRACTAL PROPERTIES OF CHAOTIC MAPS

Authors

  • Ludmila Olegovna Kirichenko Kharkiv National University of radioelectronics pr. Lenina,14, Kharkiv, Ukraine, 61166., Ukraine
  • Nadiia Viktorivna Ostroverkh Kharkiv National University of radioelectronics pr. Lenina,14, Kharkiv, Ukraine, 61166., Ukraine
  • Anna Vyacheslavovna Timko Kharkiv National University of radioelectronics pr. Lenina,14, Kharkiv, Ukraine, 61166., Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2012.4170

Keywords:

chaotic dynamic, system’s attractor, multifractal, the RR-intervals.

Abstract

In this paper a numerical investigation of multifractal properties of the attractors of nonlinear discrete systems for diverse chaotic regimes is carried out. Also a multifractal analysis of RR-interval’s sequences of human heart rate was conducted before and after using a drugs.

Author Biographies

Ludmila Olegovna Kirichenko, Kharkiv National University of radioelectronics pr. Lenina,14, Kharkiv, Ukraine, 61166.

Ph.D., Associate professor

Department of Applied mathematics

Nadiia Viktorivna Ostroverkh, Kharkiv National University of radioelectronics pr. Lenina,14, Kharkiv, Ukraine, 61166.

Student

Department of Applied mathematics

Anna Vyacheslavovna Timko, Kharkiv National University of radioelectronics pr. Lenina,14, Kharkiv, Ukraine, 61166.

Student

Department of Applied mathematics

References

  1. Мандельброт, Б. Фрактальная геометрия природы [Текст] / Б. Мандельброт – Москва–Ижевск: Институт компьютерных исследований, 2002. – 656 с.
  2. Riedi, R.H. Multifractal processes / Ed. by Doukhan P., Oppenheim G., Taqqu M.S. Long Range Dependence: Theory and Applications, P. 625–715, Birkhuser. 2002.
  3. Федер, Е. Фракталы [Текст]/ Е. Федер – М.: Мир, 1991. – 254 с.
  4. Philippe F. Is there chaos in the brain? Concepts of nonlinear dynamics and methods of investigation / Philippe F., Henri K. // Life Sciences – 2001.-324:773–793.
  5. Hoyer D., Nonlinear analysis of heart rate and respiratory dynamics / Hoyer D, Schmidt K, Bauer R, Zwiener U, Kohler M, Luthke B, Eiselt M. // IEEE Engineering in Medicine and Biology Magazine - 1997;16:31–39.
  6. Мун, Ф., Хаотические колебания / Мун Ф. - М.: Мир, 1990.
  7. Шустер, Г. Детерминированный хаос: Введение [Текст]/ Шустер Г. -М.:Мир, 1988.
  8. Patrick Flandrin. Scale Invariance and Wavelets / Patrick Flandrin, Paulo Gonзalves and Patrice Abry in Scaling, Fractals and Wavelets. Ed. by P. Abry, P. Gonçalves, J. Lévy Véhel. John Wiley & Sons, London, - 2009.
  9. Божокин, С.В. Фракталы и мультифракталы [Текст]/ С.В. Божокин, Д. А. Паршин. – Ижевск: НИЦ «Регулярпая и хаотическая динамика». – 2001. – 128 с.
  10. Kantelhardt W. Fractal and Multifractal Time Series – 2008: [Электронный ресурс]- Режим доступа: http://arxiv.org/abs/08-04.0747.
  11. Малла, С. Вэйвлеты в обработке сигналов [Текст]/ Малла С. - М.: Мир. 2005. – 671 с.
  12. Павлов, А.Н. Мультифрактальный анализ сигналов [Текст]/ А.Н. Павлов, В.С. Анищенко // Известия Саратовского университета. Серия «Физика». - 2007. -Т. 7. -Вып. 1.-С.3-25.
  13. PhysioNet: the research resource for complex physiologic signals [Электронный ресурс]- Режим доступа: www.physionet.org.

Downloads

Published

2012-06-01

How to Cite

Kirichenko, L. O., Ostroverkh, N. V., & Timko, A. V. (2012). ANALYSIS OF MULTIFRACTAL PROPERTIES OF CHAOTIC MAPS. Eastern-European Journal of Enterprise Technologies, 3(9(57), 53–58. https://doi.org/10.15587/1729-4061.2012.4170

Issue

Vol. 3 No. 9(57) (2012): Information and control systems

Section

Information and controlling system

License

Copyright (c) 2014 Ludmila Olegovna Kirichenko, Nadiia Viktorivna Ostroverkh, Anna Vyacheslavovna Timko

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.