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

Cite this article as:

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


Method for calculation of lyapunov exponents spectrum from data series

Perederij Jurij Andreevich, Saratov State University

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.


1. Кузнецов С.П. Динамический хаос. Москва: Физматлит, 2001. 2. Кузнецов С.П., Трубецков Д.И. Хаос и гиперхаос в лампе обратной волны // Известия вузов. Радиофизика. 2004. Т. XLVII. No 5. C. 1. 3. Hramov A.E., Koronovskii A.A. Generalized synchronization: A modified system approach // Phys. Rev. E. 2005. Vol. 71, No 6. 067201. 4. Pecora L.M., Carroll T.L., Heagy J.F. Statistics for mathematical properties of maps between time series embeddings // Phys. Rev. E. 1995. Vol. 52, No 4. P. 3420. 5. Hramov A. E., Koronovskii A. A., Moskalenko O. I. Are generalized synchronization and noise-induced synchronization identical types of synchronous behavior of chaotic oscillators? // Phys. Lett. A. 2006. Vol. 354, No 5–6. P. 423. 6. Wolf A., Swift J.B., Swinney H.L., Vastano J.A. Determining Lyapunov exponents from a time series // Physica D. 1985. Vol. 16. P. 285. 7. Eckmann J.-P., Kamphorst S.O., Ruelle D., Ciliberto S. Liapunov exponents from time series // Phys. Rev. A. 1986. Vol. 34, No 6. P. 4971. 8. Abarbanel H.D.I. Computing the Lyapunov spectrum of a dynamical system from an observed time series // Phys. Rev. A. 1991. Vol. 43, No 6. P. 2787. 9. Dieci L., van Vleck E.S. Computation of a few Lyapunov exponents for continuous and discrete dynamical systems // Applied Numerical Mathematics. 1995. Vol. 17. P. 275. 10. Lai D., Chen G. Statistical analysis of Lyapunov exponents from time series: A Jaco-bian approach // Mathl. Comput. Modelling 1998. Vol. 27, No 7. P. 1. 11. Rosenstein M.T., Collins J.J. De Luca C.J. A practical method for calculating largest Lyapunov exponents from small data sets // Physica D. 1993. Vol. 65, No 1–2. P. 117.  

Short text (in English):