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

For citation:

Koronovskii A. A., Hramov A. E. An introduction tо continuous wavelet analysis for specialists in field of nonlinear dynamics. Part 2 Routes to chaos from point of wavelet analysis. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 1, pp. 3-19. DOI: 10.18500/0869-6632-2002-10-1-3-19

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon and_2002-1-2_koronovskii_etal.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Review of Actual Problems of Nonlinear Dynamics
Article type: 
Review
UDC: 
551(551.2+583.1), 621.317, 621.385.6
DOI: 
10.18500/0869-6632-2002-10-1-3-19

An introduction tо continuous wavelet analysis for specialists in field of nonlinear dynamics. Part 2 Routes to chaos from point of wavelet analysis

Autors: 
Koronovskii Aleksei Aleksandrovich, Saratov State University
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal University
Abstract: 

This article is continuation оf the work earlier published аt the same journal. From positions of the continuous wavelet analysis the features of universal routes to the chaos realized in nonlinear finite-dimensional systems are illustrated: transition to the chaos through the bifurcation cascade оf the period doubling аnd transition to the chaos through the intermittency.

Key words: 
-
Acknowledgments: 
This work was supported by the Russian Foundation for Basic Research (grants No. 01-02-17392 and 02-02- 16531) and CRDF REC-006.
Reference: 
  1. Rossler OE. Аn equation for continuous chaos. Phys. Lett. A. 1976;57(5):397-398. DOI: 10.1016/0375-9601(76)90101-8.
  2. Takens F. Detecting strange attractors in dynamical systems and turbulence. In: Rand D, Young LS, editors. Lectures Notes in Mathematics, Warwick 1980. N.Y.: Springler-Verlag; 1981. P. 366-381. DOI: 10.1007/BFb0091924.
  3. Koronovsky AA, Khramov AE. Introduction to continuous wavelet analysis for specialists in the field of nonlinear dynamics. Part 1. Izvestiya VUZ. Applied Nonlinear Dynamics. 2001;9(4-5):3 (in Russian).
  4. Manneville Р, Pomeau Y. Different ways to turbulence in dissipative dynamical system. Physica D. 1980;1(2):219-226. DOI: 10.1016/0167-2789(80)90013-5.
  5. Manneville P, Pomeau Y. Intermittent transition to turbulence in dissipative dynamical system. Comm. Math. Phys. 1980;74(2):189-197. DOI: 10.1007/BF01197757.
  6. Lorenz EN. Determenistic nonperiodical flow. J. Atmos. Sci. 1963;20(2):130-141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
  7. Manneville Р, Pomeau Y. Intermittency and the Lorenz model. Phys. Lett. A. 1979;75(1-2):1-2. DOI: 10.1016/0375-9601(79)90255-X.
  8. Schuster HG. Deterministic Chaos. An Introduction. Weinheim: Physik-Verlag; 1984. 220 p.
  9. Bergé P, Pomeau Y, Vidal C. Order within Chaos: Towards a Deterministic Approach to Turbulence. New York: John Wiley & Sons; 1984. 329 p.
  10. Anfinogentov VG, Koronovsky AA, Khramov AE. Wavelet analysis and its use for analyzing the dynamics of nonlinear dynamic systems of various natures. Bulletin of the Russian Academy of Sciences: Physics. 2000;64(12):2383-2390 (in Russian).
  11. Koronovskii AA, Khramov AE. An effective wavelet analysis of the transition to chaos via intermittency. Tech. Phys. Lett. 2001;27(1):1-5. DOI: 10.1134/1.1345150.
Received: 
18.01.2002
Accepted: 
10.02.2002
Available online: 
13.12.2023
Published: 
31.07.2002
  • 233 reads