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


For citation:

Perederij J. A. Method for calculation of lyapunov exponents spectrum from data series. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 1, pp. 99-104. DOI: 10.18500/0869-6632-2012-20-1-99-104

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 155)
Language: 
Russian
Article type: 
Article
UDC: 
517.9

Method for calculation of lyapunov exponents spectrum from data series

Autors: 
Perederij Jurij Andreevich, Saratov State University
Abstract: 

The new method for the calculating of the spectrum of the Lyapunov exponents from data series is proposed. The already known methods of the same thematic are investigated. The Roessler system is given as an example for describing the proposed method. The results of numerical modeling are presented.

Reference: 
  1. Kuznetsov SP. Dynamical Chaos: Course of Lectures. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
  2. Kuznetsov SP, Trubetskov DI. Chaos and Hyperchaos in a Backward-Wave Oscillator. Radiophysics and Quantum Electronics. 2004;47:341–355. DOI: 10.1023/B:RAQE.0000046309.49269.af.
  3. Hramov AE, Koronovskii AA. Generalized synchronization: A modified system approach. Phys. Rev. E. 2005;71(6):067201. DOI: 10.1103/PhysRevE.71.067201.
  4. Pecora LM, Carroll TL, Heagy JF. Statistics for mathematical properties of maps between time series embeddings. Phys. Rev. E. 1995;52(4):3420–3439. DOI: 10.1103/physreve.52.3420.
  5. Hramov AE, Koronovskii AA, Moskalenko OI. Are generalized synchronization and noise-induced synchronization identical types of synchronous behavior of chaotic oscillators? Phys. Lett. A. 2006;354(5–6):423–427. DOI: 10.1016/j.physleta.2006.01.079.
  6. Wolf A, Swift JB, Swinney HL, Vastano JA. Determining Lyapunov exponents from a time series. Physica D. 1985;16(3):285–317. DOI: 10.1016/0167-2789(85)90011-9.
  7. Eckmann JP, Kamphorst SO, Ruelle D, Ciliberto S. Liapunov exponents from time series. Phys. Rev. A. 1986;34(6):4971–4979. DOI: 10.1103/physreva.34.4971.
  8. Brown R, Bryant P, Abarbanel HDI. Computing the Lyapunov spectrum of a dynamical system from an observed time series. Phys. Rev. A. 1991;43(6):2787–2806. DOI: 10.1103/physreva.43.2787.
  9. Dieci L, van Vleck ES. Computation of a few Lyapunov exponents for continuous and discrete dynamical systems. Applied Numerical Mathematics. 1995;17:275–291. DOI: 10.1016/0168-9274(95)00033-Q.
  10. Lai D, Chen G. Statistical analysis of Lyapunov exponents from time series: A Jacobian approach. Math. Comput. Modelling. 1998;27(7):1–9. DOI: 10.1016/S0895-7177(98)00032-6.
  11. Rosenstein MT, Collins JJ. De Luca CJ. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D. 1993;65(1–2):117–134. DOI: 10.1016/0167-2789(93)90009-P.  
Received: 
29.12.2011
Accepted: 
29.12.2011
Published: 
20.04.2012
Short text (in English):
(downloads: 74)