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

For citation:

Bezruchko B. P., Smirnov D. A. Method for reconstruction of equations with harmonic driving from time series. Izvestiya VUZ. Applied Nonlinear Dynamics, 2001, vol. 9, iss. 2, pp. 27-38. DOI: 10.18500/0869-6632-2001-9-2-27-38

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 2001no2p027.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2001-9-2-27-38

Method for reconstruction of equations with harmonic driving from time series

Autors: 
Bezruchko Boris Petrovich, Saratov State University
Smirnov Dmitrij Alekseevich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

We propose a general approach to constructing global models of harmonically driven systems from time series. It is a modification of the standard method of global reconstruction of differential equations - a polynomial, which arguments are sequential derivatives of an observable along with explicit functions of time, enters in model equations. Efficiency and details of the approach are demonstrated by various numerical examples.

Key words: 
-
Acknowledgments: 
The work was supported by the American Foundation for Civic Research and Development (grant RЕС-006) and RFBR (grants гранты 99-02-17735 and 01-02-06039).
Reference: 
  1. Cremers J, Hubler А. Construction оf differential equations from experimental data. Z. Naturforschung А. 1987;42:797–802. DOI: 10.1515/zna-1987-0805.
  2. Baake E, Baake M, Bock HJ, Briggs KM. Fitting ordinary differential equations to chaotic data. Phys. Rev. A. 1992;45(8):5524–5529. DOI: 10.1103/PhysRevA.45.5524.
  3. Brown R, Rulkov NF, Tracy ER. Modeling and synchronizing chaotic systems from time-series data. Phys. Rev. В. 1994;49:3784–3800. DOI: 10.1103/PhysRevE.49.3784.
  4. Gouesbet G, Letellier С. Global vector-field approximation by using а multivariate polynomial L2 approximation on nets. Phys. Rev. E. 1994;49:4955. DOI: 10.1103/PhysRevE.49.4955.
  5. Gribkov DA, Gribkova BB, Kravtsov SA, Kuznetsov YI, Rzhanov AG. Restoration of dynamic system structure by time series. Radiotekhnika i elektronika. 1994;39(2):269–277.
  6. Janson NB, Anishchenko BC. Modeling of dynamic systems on experimental data. Izvestiya VUZ. Applied nonlinear dynamics. 1995;3(3):112.
  7. Pavlov AH, Janson NB, Anishchenko BC. Application of statistical methods in solving the problem of global reconstruction. Tech. Phys. Lett. 1997;23(8):7–13.
  8. Kadtke J. Classification оf highly noisy signals using global dynamical models. Phys. Lett. А. 1995;203:196–202. DOI: 10.1016/0375-9601(95)00375-D.
  9. Kadtke J, Kremliovsky M. Estimating statistics for detecting determinism using global dynamical models. Phys. Lett. A. 1997;229:97–106. DOI:10.1016/S0375-9601(97)00149-7.
  10. Gouesbet G, Maquet J. Construction of phenomenological models from numerical scalar time series. Physica D. 1992;58:202–215. DOI: 10.1016/0167-2789(92)90109-Z.
  11. Hegger R, Kantz H, Schmuser F, Diestelhorst M, Kapsch R-P, Beige H. Dynamical properties of a ferroelectric capacitors observed through nonlinear time series analysis. Chaos. 1998;8(3):727–736. DOI: 10.1063/1.166356.
  12. Bezruchko BP, Dikanev TB, Seleznev EP, Smirnov D.A. Restoration of differential equations of non-autonomous dynamic system by experimental data. In.: Tech. doc. of V. International School "Chaotic Auto-Oscillations and Structure Formation - KHAOS'98".  1998, Saratov, Russia. 68-69 p.
  13. Bezruchko BP, Seleznev EP, Smirnov DA. Reconstruction of equations of nonautonomous nonlinear oscillator by time series: models, experiment. Izvestiya VUZ. Applied nonlinear dynamics. 1999;7(1):49–68.
  14. Farmer JD, Sidorowich JJ. Predicting chaotic time series. Phys. Rev. Lett. 1987;59:845–848. DOI: 10.1103/PhysRevLett.59.845.
  15. Anishchenko BS, Vadivasova TE, Astakhov BB. Nonlinear Dynamics of Chaotic and Stochastic Systems. Saratov University Publishing, 1999. 368 p.
  16. Takens F. Detecting strange attractors in turbulence. Dynamical systems and turbulence. In.: Rang D, Young LS, editors. Lecture notes in mathematics. USA: Warwick; 1980;898:366.
  17. Sauer T, Yorke JА, Casdagli М. Embedology. J. Statist. Phys. 1991;65:579–616. DOI: 10.1007/BF01053745.
  18. Hasler M. Electrical circuits with chaotic behavior. Proceedings оf the IEEE. 1987;75:40. DOI: 10.1109/PROC.1987.13846n.
Received: 
19.12.2000
Accepted: 
18.05.2001
Published: 
17.07.2001
  • 326 reads