From: pecora@zoltar.nrl.navy.mil (Louis M. Pecora) Newsgroups: sci.math.num-analysis Subject: Re: Liapunov-Exponents? Date: Mon, 02 Nov 1998 14:38:07 -0500 In article <362D157D.A0104753@sol.rutgers.edu>, Johannes Khinast wrote: > Hi: > > Does anyone know a reliable Fortran code for computing Lyapunov > exponents of > a time series? > Please email to: khinast@sol.rutgers.edu I strongly suggest you _do not_ use canned routines, but write your own. I speak from experience. Nonlinear time series analysis is a fascinating area of research, but many of the techniques have not yet reached the black-box stage such as for FFT. For that reason you can get someone's routine, put in a good time series and get crap out, but you won't know it. Better to write your own, learn the problems, and test it on the types of data you will use. There are also related issues you must learn to deal with, such as what dimension do I use for the reconstruction? I would highly recommend the books: Nonlinear Time Series Analysis by Kantz and Schreiber, Cambridge U. Press, 1997 This is a very good book from introduction up to advanced topics. Analysis of Observed Chaotic Data by H.D.I. Abarbanel (Springer, New York, 1996). Practical Numerical Algorithms for Chaotic Systems by T.S. Parker and L.O. Chua (Springer-Verlag, New York, 1989). "Nonlinear Dynamics and Time Series: Building a Bridge between the Natural and Statistical Sciences, ed. by Colleen D. Cutler and Daniel T. Kaplan, (American Mathematical Society,, Providence RI, 1997), Vol. Fields Institute Communications, Volume 11, 1997., pp. 260. A good proceedings that deals with lots of time series issues. Some related papers are: [1] R. Brown and P. Bryant, "Computing the Lyapunov spectrum of a dynamical system from an observed time series," Physical Review A 43, 2787 (1991). [2] J.-P. Eckmann, S.O. Kamphorst, D. Ruelle et al., "Liapunov exponents from time series," Physical Review A 34, 4971 (1986). [3] A. Wolf, J.B. Swift, H.L. Swinney et al., "Determining Lyapunov Exponents from a Time Series," Physica 16D, 285-317 (1985). Be aware that the original Wolf method was flawed, but he has a new method that apparently works well. Check his web site at the Cooper Union College, NY, USA (sorry, I don't have the address). -- Louis M. Pecora pecora@zoltar.nrl.navy.mil == My views and opinions are not those of the U.S. Navy. == == No Spamming or Soliciting -- both are illegal at this site == --------------------------------------------------------------------- Check out our Nonlinear Web site: http://code6343.nrl.navy.mil/ -------------------------------------------------------------------- ------------------------------------------------------------------------ * The 5th Experimental Chaos Conference Torino Italy 21-25 June 1999. Check it out at http://www.physics.gatech.edu/ecc5/#proceedings * The 4th Experimental Chaos Conference Sessions & Abstracts Online: http://natasha.umsl.edu/Exp_Chaos4, proceedings coming in a few months. ---------------------------------------------------------------------