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

For citation:

Namajunas A. M., Tamashjavichjus A. V. Measurement of correlation dimension from time series. Izvestiya VUZ. Applied Nonlinear Dynamics, 1993, vol. 1, iss. 1, pp. 104-108. DOI: 10.18500/0869-6632-1993-1-1-104-108

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 1993no1-2p104.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
621.317.7
DOI: 
10.18500/0869-6632-1993-1-1-104-108

Measurement of correlation dimension from time series

Autors: 
Namajunas A. M., Vilnius Institute of Semiconductor Physics
Tamashjavichjus A. V., Vilnius Institute of Semiconductor Physics
Abstract: 

An electronic technique for determining the correlation dimension of strange attractors from a single observable is described. In contrast to the conventional computer methods the elaborated electronic instrument operates on a real time scale. Mathematical description of the procedure as well as the block diagram of the instrument are presented. The correlation dimension is measured for a chaotic oscillator which is a standard LC-oscillator containing an additional nonlinear inertial chain. There is a good agreement of the experimental result with the numerical calculations carried out for the corresponding dynamical equations. In addition, the periodic oscillations and random noise are analyzed electronically for comparison.

Key words: 
-
Reference: 
  1. Neimark YuI, Landa PS. Stochastic and Chaotic Osciliations. Dordrecht: Springer; 1992. 500 p. DOI: 10.1007/978-94-011-2596-3.
  2. Mayer-Kress G, editor. Dimensions and Entropies in Chaotic Systems. Berlin: Springer; 1981. 266 p.
  3. Grassberger P, Procaccia I. Characterization of strange attractors. Phys. Rev. Lett. 1983;50(5):346-349. DOI: 10.1103/PhysRevLett.50.346
  4. Lee C-K, Moon FC. An optical technique for measuring fractal dimensions of planar Poincare maps. Phys. Lett. A. 1986;114(5):222-226. DOI: 10.1016/0375-9601(86)90211-2
  5. Namajunas A, Pozela J, Tamasevicius A. An electronic technique for measuring phase space dimension from chaotic time series. Phys. Lett. A. 1988;131(2):85-90. DOI: 10.1016/0375-9601(88)90661-5
  6. Packard NH, Crutchfield JP, Farmer JD, Shaw RS. Geometry from a time series. Phys. Rev. Lett. 1980;45(9):712-716. DOI: 10.1103/PhysRevLett.45.712
  7. Pikshiris RА, Piragas KA, Tomashkyavishyus AV. Schemes for converting an LC autogenerator into a noise generator. Radio engineering. 1986;(9):43.
  8. Agarwal AK, Banerjee К, Bhattacharjee JK. Universality of fractal dimension at the onset of period-doubling Chaos. Phys. Lett. A. 1986;119(6):280-282. DOI: 10.1016/0375-9601(86)90147-7.
Received: 
11.03.1993
Accepted: 
12.04.1993
Published: 
20.07.1993
  • 1692 reads