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

For citation:

Sonechkin D. M. Identification of the periodic trajectories and attractors description by time series. Izvestiya VUZ. Applied Nonlinear Dynamics, 1993, vol. 1, iss. 1, pp. 50-56. DOI: 10.18500/0869-6632-1993-1-1-50-56

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 1993no1-2p050.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
621.317
DOI: 
10.18500/0869-6632-1993-1-1-50-56

Identification of the periodic trajectories and attractors description by time series

Autors: 
Sonechkin Dmitrij Mihajlovich, Hydrometeorological Research Centre of Russian Federation
Abstract: 

The results of calculation of dimensions and identification of periodic trajectories by time series of meteorological data considered as series of trajectories of chaotic dynamic system are described.

Key words: 
-
Reference: 
  1. Nicolis С, Nicolis G. Is there a climatic attractor? Nature. 1984;311:529-532. DOI: 10.1038/311529a0
  2. Grassberger P. Do climatic attractor exist? Nature. 1986;323:609-612. DOI: 10.1038/323609a0
  3. Lorenz EN. Dimension of weather and climatic attractors. Nature. 1991;353:241-244. DOI: 10.1038/353241a0
  4. Sonechkin DМ. On the assessment of the number of degrees of freedom of large-scale atmospheric processes. Proc. Hydrometeorological Centre of the USSR. 1987;290:27-39.
  5. Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Berlin: Springer; 1988. 500 p. DOI: 10.1007/978-1-4684-0313-8
  6. Pawelzik К, Schuster НС. Generalized dimensions and entropies from a measured time series. Phys. Rev. A. 1987;35(1):481-484. DOI: 10.1103/PhysRevA.35.481
  7. Badii R, Politi A. Hausdorf dimension and uniformity factor of strange attractors. Phys. Rev. Lett. 1984;52(19):1661-1664. DOI: 10.1103/PhysRevLett.52.1661
  8. Grassberger P. Finite sample corrections to entropy and dimension estimates. Phys. Lett. A. 1988;128(6-7):369-373. DOI: 10.1016/0375-9601(88)90193-4
  9. Vinogradskaya АА, Zimin NE, Sonechkin DМ. The maximum possibilities of long-term weather forecast based on archived data. Meteorology and Hydrology. 1990;10:5-12.
  10. Farmer JD, Sidorowich JJ. Predicting chaotic time series. Phys. Rev. Lett. 1987;59(8):845-848. DOI: 10.1103/PhysRevLett.59.845
  11. Sugihara G, May КМ. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature. 1990;344:734-741. DOI: 10.1038/344734a0
  12. Abarbanel HDI, Brown R, Kadtke JB. Prediction in chaotic nonlinear systems: methods for time series with broadband Fourier spectra. Phys. Rev. A. 1990;41(4):1782-1807. DOI: 10.1103/PhysRevA.41.1782
  13. Procaccia I. Universal propeties of dynamically complex systems: the organization of chaos. Nature. 1988;333:618-623. DOI: 10.1038/333618a0
  14. Auerbach D, Cvitanovic P, Eckmann J-P, Gunaratne G, Procaccia I. Exploring chaotic motion through periodic orbits. Phys. Rev. Lett. 1987;58(23):2387-2389. DOI: 10.1103/PhysRevLett.58.2387
  15. Mindlir СВ, Hou X-J, Solari HG, Gilmore R, Tufillaro NB. Classification of strange attractors by integers. Phys. Rev. Lett. 1990;64(20):2350-2353. DOI: 10.1103/PhysRevLett.64.2350
  16. Vinogradskaya АА, et al. Theory of the annual course of zonal circulation of the atmosphere. 2. Fourteen-mode model of sub- and superharmonic resonances. Proc. Hydrometeorological Centre of the USSR. 1988;297:166.
Received: 
23.02.1993
Accepted: 
20.04.1993
Published: 
20.07.1993
  • 1667 reads