Lyapunov exponents

Massimo Pigliucci pigliucc at uconnvm.bitnet
Fri Mar 12 11:38:28 EST 1993


  Dear Netters,

                    a few weeks ago I posted a message on this
network looking for references to software dealing with the
determination of Lyapunov exponents for the study of chaos in
experimental data. I also asked in general for software dealing
with non-linear dynamics. I'd like to share the results of this
search, given that many people have expressed the desire to be
kept informed about it. I added also software packages of which I
was already aware.

1)   TraX, distributed by Exeter Software, 100 North Country Rd.,
Setauket NY 11733. This is a comprehensive package developed by
V.V. Levitin that deals with simulation of theoretical models
using a variety of NLD techniques. It can display time series,
phase plots, obtain bifurcation diagrams, compute Poincare`
sections, Lyapunov exponents and maximu-return map. The manual is
not easy to understan and far from complete. Very good graphics
options, underutilized because of the lack of a printer interface
(you can export your results as an ASCII file). It costs around
$250.

2)   Insite, distributed by Insite software, P.O. Box 9662,
Berkeley, CA 94709. Written by T.S. Parker, it is basically the
companion to the highly technical, but very well written, Parker
& Chua, "Practical numerical algorithms for chaotic systems",
Springer-Verlag. It's a powerful piece of software, that requires
some familiarity with programming and with NLD theory in general.
It comes for about $400 (to which, however, you have to add the
costs of a C compiler, a MetaWindows metagraphics program and
Metagraphics libraries).

3)   Specific on Lyapunov exponents: Wolf et al. (Physyca 16D,
1985) published the listing - in Fortran - of two programs, one
for models, the second for experimental data series. Wolf
(currently at the Physics Department, The Cooper Union, Cooper
Square, New York NY 10003) has been so kind to send me un updated
copy in Fortran, C and executable version for PCs. The program
comes with a good manual, for free (besides expendes).

4)   Still on Lyapunov exponents: Stephen Ellner has also been so
kind as to give me access to
his files via e-mail (he is at the Biomathematics program, Dept.
of Statistics, N.C. State University, Raleigh, NC 27695). His
program is based on the algorithm published in Nychka et al.
(Journal of the Royal Statistical Society B54, 1992).

5)   Alan Hastings (Division of Environmental Studies & Institute
of Theoretical Dynamics, University of California, Davis CA
95616) has sent me a copy of a review on chaos in ecology to be
published on the Annual Review of Ecology and Systematics. The MS
is plenty of references to methodological papers on chaos theory.

6)   Wolf (see above) is also author of an educational software
called "Chaos simulations", distributed for $70 by Physics
Academic Software, Dept. of Physics, North Carolina State
University, Raleigh, NC 27695. The same publishers also
distributes other two titles of interest: Chaos demonstrations
and Chaotic dynamics workbench, both at $70 (each).

7)   Finally (and that was the purpose of it all), I just
finished a methodological review on the subject. Anybody
interested in receiving the manuscript on the "nuts and bolts" of
NLD, please give me a call, drop me a note, or send me a bit.

     I hope this info is going to be useful to someone. Chaos be
with you. (Massimo Pigliucci)

**********************************************************************
MASSIMO PIGLIUCCI
DEPARTMENT OF ECOLOGY AND EVOLUTIONARY BIOLOGY
UNIVERSITY OF CONNECTICUT, STORRS CT 06269
PHONE: 203-486-4372 / FAX: 203-486-6364
BITNET: PIGLIUCC at UCONNVM / INTERNET: PIGLIUCC at UCONNVM.UCONN.EDU

"THIS IS BECOMING REALLY INSIGNIFICANT". "NOT ENOUGH".
(SAMUEL BECKETT, WAITING FOR GODOT)
**********************************************************************



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