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Section B

A detailed study of the Wolf's algorithm

, &
Pages 1135-1148 | Received 13 Jul 2006, Accepted 02 Oct 2007, Published online: 17 Jun 2009

References

  • Alligood , K. , Sauer , T. and Yorke , J. 1996 . Chaos – An introduction to Dynamical Systems , Springer Verlag . ISBN 0-387-94677-2
  • Brown , R. , Bryant , P. and Abarbanel , H. D. 1991 . Computing the Lyapunov spectrun of a dynamical system from an observed time series . Phys. Rev. A , 43 ( 6 ) : 2787 – 2806 .
  • Bryant , P. , Brown , R. and Abarbanel , H. D. 1990 . Lyapunov exponents from observed time series . Phys. Rev. Lett , 65 ( 13 ) : 1523 – 1526 .
  • Chistianssen , F. and Rugh , H. H. 1997 . Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization . Nonlinearity , 10 : 1063 – 1072 .
  • Diakonos , F. K. , Pingel , D. and Schmelcher , P. 2000 . Analysing Lyapunov spectra of chaotic dynamical systems . Phys. Rev. E , 62 ( 3 ) : 4413 – 4416 .
  • Grond , F. 2003 . “ A Robust, Locally Interpretable Algorithm for Liapunov Exponents ” . Vol. 16 , 841 – 852 . Chaos : Solitons and Fractals .
  • Hegger , R. 1999 . Estimating the Lyapunov spectrum of time delay feedback systems from scalar time series . Phys. Rev. E , 60 ( 2 ) : 1563 – 1566 .
  • Janaki , T. M. 1999 . Computation of the Lyapunov spectrum for continuous time dynamical system and discrete maps . Phys. Rev. E , 60 ( 5 ) : 6614 – 6626 .
  • Jon , Wright . 1984 . Method for calculating a Lyapunov exponent . Phys. Rev A , 29 ( 5 ) : 2924 – 2927 .
  • Oiwa , N. N. and Fielder-Ferrara , N. 1998 . A fast algorithm for estimating Lyapunov exponents from time series . Phys. Lett. A , 246 : 117 – 121 .
  • Oiwa , N. N. and Fielder-Ferrara , N. 2002 . Lyapunov spectrum from time series using moving boxes . Phys. Rev. E , 65 ( 036702 ) : 1 – 9 .
  • Pyragas , K. 1997 . Conditional Lyapunov exponents from time series . Phys. Rev. E , 56 ( 5 ) : 5183 – 5188 .
  • Rosenstein , M. , Collins , J. J. and de Luca , C. J. 1993 . A practical method for calculating largest lyapunov exponents from small data sets . Physica D , 65 : 117 – 134 .
  • Sano , M. and Sawada , Y. 1985 . Measurement of the Lyapunov spectrum from a chaotic time series . Phys. Rev. Lett , 55 ( 10 ) : 1082 – 1085 .
  • Shibata , T. and Kaneko , K. Collective chaos . Phys. Rev. Lett , 81 ( 19 ) 4116 – 4119 .
  • von Bremen , H. F. , Udwadia , F. E. and Proskurowski , W. 1997 . An efficient QR method for the computation of Lyapunov exponents . Physica D , 101 : 1 – 16 .
  • Wolf , A. 1985 . Determining Lyapunov exponents from a time series . Physica 16D , : 285 – 317 .

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