|
|
| Home > Science > sci > |
Nonlinear Science FAQ |
Section 3 of 4 - Prev - Next
All sections - 1 - 2 - 3 - 4
density, temperature, etc. Normally a gradually variation of a parameter in
the system corresponds to the gradual variation of the solutions of the
problem. However, there exists a large number of problems for which the number
of solutions changes abruptly and the structure of solution manifolds varies
dramatically when a parameter passes through some critical values. For
example, the abrupt buckling of a stab when the stress is increased beyond a
critical value, the onset of convection and turbulence when the flow
parameters are changed, the formation of patterns in certain PDE's, etc. This
kind of phenomena is called bifurcation, i.e. a qualitative change in the
behavior of solutions of a dynamics system, a partial differential equation or
a delay differential equation.
Bifurcation theory is a method for studying how solutions of a nonlinear
problem and their stability change as the parameters varies. The onset of
chaos is often studied by bifurcation theory. For example, in certain
parameterized families of one dimensional maps, chaos occurs by infinitely
many period doubling bifurcations
(See http://www.stud.ntnu.no/~berland/math/feigenbaum/)
There are a number of well constructed computer tools for studying
bifurcations. In particular see [5.2] for AUTO and DStool.
[3.18] What is a Hamiltonian Chaos?
The transition to chaos for a Hamiltonian (conservative) system is somewhat
different than that for a dissipative system (recall [2.5]). In an integrable
(nonchaotic) Hamiltonian system, the motion is "quasiperiodic", that is motion
that is oscillatory, but involves more than one independent frequency (see
also [2.12]). Geometrically the orbits move on tori, i.e. the mathematical
generalization of a donut. Examples of integrable Hamiltonian systems include
harmonic oscillators (simple mass on a spring, or systems of coupled linear
springs), the pendulum, certain special tops (for example the Euler and
Lagrange tops), and the Kepler motion of one planet around the sun.
It was expected that a typical perturbation of an integrable Hamiltonian
system would lead to "ergodic" motion, a weak version of chaos in which all of
phase space is covered, but the Lyapunov exponents [2.11] are not necessarily
positive. That this was not true was rather surprisingly discovered by one of
the first computer experiments in dynamics, that of Fermi, Pasta and Ulam.
They showed that trajectories in nonintegrable system may also be surprisingly
stable. Mathematically this was shown to be the case by the celebrated theorem
of Kolmogorov Arnold and Moser (KAM), first proposed by Kolmogorov in 1954.
The KAM theorem is rather technical, but in essence says that many of the
quasiperiodic motions are preserved under perturbations. These orbits fill out
what are called KAM tori.
An amazing extension of this result was started with the work of John Greene
in 1968. He showed that if one continues to perturb a KAM torus, it reaches a
stage where the nearby phase space [2.4] becomes self-similar (has fractal
structure [3.2]). At this point the torus is "critical," and any increase in
the perturbation destroys it. In a remarkable sequence of papers, Aubry and
Mather showed that there are still quasiperiodic orbits that exist beyond this
point, but instead of tori they cover cantor sets [3.5]. Percival actually
discovered these for an example in 1979 and named them "cantori."
Mathematicians tend to call them "Aubry-Mather" sets. These play an important
role in limiting the rate of transport through chaotic regions.
Thus, the transition to chaos in Hamiltonian systems can be thought of as the
destruction of invariant tori, and the creation of cantori. Chirikov was the
first to realize that this transition to "global chaos" was an important
physical phenomena. Local chaos also occurs in Hamiltonian systems (in the
regions between the KAM tori), and is caused by the intersection of stable and
unstable manifolds in what Poincaré called the "homoclinic trellis."
To learn more: See the introductory article by Berry, the text by Percival and
Richards and the collection of articles on Hamiltonian systems by MacKay and
Meiss [4.1]. There are a number of excellent advanced texts on Hamiltonian
dynamics, some of which are listed in [4.1], but we also mention
Meyer, K. R. and G. R. Hall (1992), Introduction to Hamiltonian dynamical
systems and the N-body problem (New York, Springer-Verlag).
[4] To Learn More
[4.1] What should I read to learn more?
Popularizations
1 Gleick, J. (1987). Chaos, the Making of a New Science.
London, Heinemann. http://www.around.com/chaos.html
2 Stewart, I. (1989). Does God Play Dice? Cambridge, Blackwell.
http://www.amazon.com/exec/obidos/ASIN/1557861064
3 Devaney, R. L. (1990). Chaos, Fractals, and Dynamics: Computer
Experiments in Mathematics. Menlo Park, Addison-Wesley
http://www.amazon.com/exec/obidos/ASIN/1878310097
4 Lorenz, E., (1994) The Essence of Chaos, Univ. of Washington Press.
http://www.amazon.com/exec/obidos/ASIN/0295975148
5 Schroeder, M. (1991) Fractals, Chaos, Power: Minutes from an infinite paradise
W. H. Freeman New York:
Introductory Texts
1 Abraham, R. H. and C. D. Shaw (1992) Dynamics: The Geometry of
Behavior, 2nd ed. Redwood City, Addison-Wesley.
2 Baker, G. L. and J. P. Gollub (1990). Chaotic Dynamics.
Cambridge, Cambridge Univ. Press.
http://www.cup.org/titles/catalogue.asp?isbn=0521471060
3 DevaneyDevaney, R. L. (1986). An Introduction to Chaotic Dynamical
Systems. Menlo Park, Benjamin/Cummings.
http://math.bu.edu/people/bob/books.html
4 Kaplan, D. and L. Glass (1995). Understanding Nonlinear Dynamics,
Springer-Verlag New York. http://www.cnd.mcgill.ca/books_understanding.html
5 Glendinning, P. (1994). Stability, Instability and Chaos.
Cambridge, Cambridge Univ Press.
http://www.cup.org/Titles/415/0521415535.html
6 Jurgens, H., H.-O. Peitgen, et al. (1993). Chaos and Fractals: New
Frontiers of Science. New York, Springer Verlag.
http://www.springer-ny.com/detail.tpl?isbn=0387979034
7 Moon, F. C. (1992). Chaotic and Fractal Dynamics. New York, John Wiley.
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471545716.html
8 Percival, I. C. and D. Richard (1982). Introduction to Dynamics. Cambridge,
Cambridge Univ. Press.
http://www.cup.org/titles/catalogue.asp?isbn=0521281490
9 Scott, A. (1999). NONLINEAR SCIENCE: Emergence and Dynamics of
Coherent Structures, Oxford http://www4.oup.co.uk/isbn/0-19-850107-2
http://www.imm.dtu.dk/documents/users/acs/BOOK1.html
10 Smith, P (1998) Explaining Chaos, Cambridge
http://us.cambridge.org/titles/catalogue.asp?isbn=0521477476
11 Strogatz, S. (1994). Nonlinear Dynamics and Chaos. Reading,
Addison-Wesley
http://www.perseusbooksgroup.com/perseus-cgi-bin/display/0-7382-0453-6
12 Thompson, J. M. T. and H. B. Stewart (1986) Nonlinear Dynamics and
Chaos. Chichester, John Wiley and Sons.
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471876844.html
13 Tufillaro, N., T. Abbott, et al. (1992). An Experimental Approach
to Nonlinear Dynamics and Chaos. Redwood City, Addison-Wesley.
http://www.amazon.com/exec/obidos/ASIN/0201554410/
14 Turcotte, Donald L. (1992). Fractals and Chaos in Geology and
Geophysics, Cambridge Univ. Press.
http://www.cup.org/titles/catalogue.asp?isbn=0521567335
Introductory Articles
1 May, R. M. (1986). "When Two and Two Do Not Make Four."
Proc. Royal Soc. B228: 241.
2 Berry, M. V. (1981). "Regularity and Chaos in Classical Mechanics,
Illustrated by Three Deformations of a Circular Billiard."
Eur. J. Phys. 2: 91-102.
3 Crawford, J. D. (1991). "Introduction to Bifurcation Theory."
Reviews of Modern Physics 63(4): 991-1038.
3 Shinbrot, T., C. Grebogi, et al. (1992). "Chaos in a Double Pendulum."
Am. J. Phys 60: 491-499.
5 David Ruelle. (1980). "Strange Attractors,"
The Mathematical Intelligencer 2: 126-37.
Advanced Texts
1 Arnold, V. I. (1978). Mathematical Methods of Classical Mechanics.
New York, Springer.
http://www.springer-ny.com/detail.tpl?isbn=038796890
2 Arrowsmith, D. K. and C. M. Place (1990), An Introduction to Dynamical Systems.
Cambridge, Cambridge University Press.
http://us.cambridge.org/titles/catalogue.asp?isbn=0521316502
3 Guckenheimer, J. and P. Holmes (1983), Nonlinear Oscillations, Dynamical
Systems, and Bifurcation of Vector Fields, Springer-Verlag New York.
4 Kantz, H., and T. Schreiber (1997). Nonlinear time series analysis.
Cambridge, Cambridge University Press
http://www.mpipks-dresden.mpg.de/~schreibe/myrefs/book.html
5 Katok, A. and B. Hasselblatt (1995), Introduction to the Modern
Theory of Dynamical Systems, Cambridge, Cambridge Univ. Press.
http://titles.cambridge.org/catalogue.asp?isbn=0521575575
6 Hilborn, R. (1994), Chaos and Nonlinear Dyanamics: an Introduction for
Scientists and Engineers, Oxford Univesity Press.
http://www4.oup.co.uk/isbn/0-19-850723-2
7 Lichtenberg, A.J. and M. A. Lieberman (1983), Regular and Chaotic Motion,
Springer-Verlag, New York .
8 Lind, D. and Marcus, B. (1995) An Introduction to Symbolic Dynamics and
Coding, Cambridge University Press, Cambridge
http://www.math.washington.edu/SymbolicDynamics/
9 MacKay, R.S and J.D. Meiss (eds) (1987), Hamiltonian Dynamical Systems
A reprint selection, , Adam Hilger, Bristol
10 Nayfeh, A.H. and B. Balachandran (1995), Applied Nonlinear Dynamics:
Analytical, Computational and Experimental Methods
John Wiley& Sons Inc., New York
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471593486.html
11 Ott, E. (1993). Chaos in Dynamical Systems. Cambridge University Press,
Cambridge. http://us.cambridge.org/titles/catalogue.asp?isbn=0521010845
12 L.E. Reichl, (1992), The Transition to Chaos, in Conservative and
Classical Systems: Quantum Manifestations Springer-Verlag, New York
13 Robinson, C. (1999), Dynamical Systems: Stability, Symbolic
Dynamics, and Chaos, 2nd Edition, Boca Raton, CRC Press.
http://www.crcpress.com/shopping_cart/products/product_detail.asp?sku=8495
14 Ruelle, D. (1989), Elements of Differentiable Dynamics and Bifurcation
Theory, Academic Press Inc.
15 Tabor, M. (1989), Chaos and Integrability in Nonlinear Dynamics:
an Introduction, Wiley, New York.
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471827282.html
16 Wiggins, S. (1990), Introduction to Applied Nonlinear Dynamical Systems
and Chaos, Springer-Verlag New York.
17 Wiggins, S. (1988), Global Bifurcations and Chaos, Springer-Verlag New
York.
[4.2] What technical journals have nonlinear science articles?
Physica D The premier journal in Applied Nonlinear Dynamics
Nonlinearity Good mix, with a mathematical bias
Chaos AIP Journal, with a good physical bent
SIAM J. of Dynamical Systems Online Journal with multimedia
http://www.siam.org/journals/siads/siads.htm
Chaos Solitons and Fractals Low quality, some good applications
Communications in Math Phys an occasional paper on dynamics
Comm. in Nonlinear Sci. New Elsevier journal
and Num. Sim. http://www.elsevier.com/locate/cnsns
Ergodic Theory and Rigorous mathematics, and careful work
Dynamical Systems
International J of lots of color pictures, variable quality.
Bifurcation and Chaos
J Differential Equations A premier journal, but very mathematical
J Dynamics and Diff. Eq. Good, more focused version of the above
J Dynamics and Stability Focused on Eng. applications. New editorial
of Systems board--stay tuned.
J Fluid Mechanics Some expt. papers, e.g. transition to turbulence
J Nonlinear Science a newer journal--haven't read enough yet.
J Statistical Physics Used to contain seminal dynamical systems papers
Nonlinear Dynamics Haven't read enough to form an opinion
Nonlinear Science Today Weekly News: http://www.springer-ny.com/nst/
Nonlinear Processes in New, variable quality...may be improving
Geophysics
Physics Letters A Has a good nonlinear science section
Physical Review E Lots of Physics articles with nonlinear emphasis
Regular and Chaotic Dynamics Russian Journal http://web.uni.udm.ru/~rcd/
[4.3] What are net sites for nonlinear science materials?
Bibliography
http://www.uni-mainz.de/FB/Physik/Chaos/chaosbib.html Mainz http site
ftp://ftp.uni-mainz.de/pub/chaos/chaosbib/ Mainz ftp site
http://www-chaos.umd.edu/publications/searchbib.html Seach the Mainz Site
http://www-chaos.umd.edu/publications/references.html Maryland
http://www.cpm.mmu.ac.uk/~bruce/combib/ Complexity Bibliography
http://www.mth.uea.ac.uk/~h720/research/ Ergodic Theory and Dynamical Systems
http://www.drchaos.net/drchaos/intro.html Nonlinear Dynamics Resources (pdf file)
http://www.nonlin.tu-muenchen.de/chaos/Projects/miguelbib Sanjuan's Bibliography
Preprint Archives
http://www.math.sunysb.edu/dynamics/preprints/ StonyBrook
http://cnls.lanl.gov/People/nbt/intro.html Los Alamos Preprint Server
http://xxx.lanl.gov/ Nonlinear Science Eprint Server
http://www.ma.utexas.edu/mp_arc/mp_arc-home.html Math-Physics Archive
http://www.ams.org/global-preprints/ AMS Preprint Servers List
Conference Announcements
http://at.yorku.ca/amca/conferen.htm Mathematics Conference List
http://www.math.sunysb.edu/dynamics/conferences/conferences.html
StonyBrook List
http://www.nonlin.tu-muenchen.de/chaos/termine.html Munich List
http://xxx.lanl.gov/Announce/Conference/ Los Alamos List
http://www.tam.uiuc.edu/Events/conferences.html Theoretical & Applied Mechanics
http://www.siam.org/meetings/ds99/index.htm SIAM Dynamical Systems 1999
Newsletters
gopher://gopher.siam.org:70/11/siag/ds SIAM Dynamical Systems Group
http://www.amsta.leeds.ac.uk/Applied/news.dir/ UK Nonlinear News
Education Sites
http://math.bu.edu/DYSYS/ Devaney's Dynamical Systems Project
Electronic Journals
http://www.springer-ny.com/nst/ Nonlinear Science Today
http://www3.interscience.wiley.com/cgi-bin/jtoc?ID=38804 Complexity
http://journal-ci.csse.monash.edu.au/ Complexity International Journal
Electronic Texts
http://cnls.lanl.gov/People/nbt//Book/node1.html An experimental approach
to nonlinear dynamics and chaos
http://www.nbi.dk/~predrag/QCcourse/ Lecture Notes on Periodic Orbits
http://hypertextbook.com/chaos/ The Chaos HyperTextBook
Institutes and Academic Programs
http://physicsweb.org/resources/dsearch.phtml Physics Institutes
http://ip-service.com/WiW/institutes.html Nonlinear Groups
http://www-chaos.engr.utk.edu/related.html Research Groups in Chaos
Java Applets Sites
http://physics.hallym.ac.kr/education/TIPTOP/VLAB/about.html Virtual Laboratory
http://monet.physik.unibas.ch/~elmer/pendulum/ Java Pendulum
http://kogs-www.informatik.uni-hamburg.de/~wiemker/applets/fastfrac/fastfrac.html
Java Fractal Explorer
http://www.apmaths.uwo.ca/~bfraser/index.html B. Fraser¹s Nonlinear Lab
http://www.cmp.caltech.edu/~mcc/Chaos_Course/ Mike Cross' Demos
Who is Who in Nonlinear Dynamics
http://www.chaos-gruppe.de/wiw/wiw.html Munich List
http://www.math.sunysb.edu/dynamics/people/list.html Stonybrook List
Lists of Nonlinear sites
http://makeashorterlink.com/?C58C23C16 Netscape¹s List
http://cnls.lanl.gov/People/nbt/sites.html Tufillaro's List
http://cires.colorado.edu/people/peckham.scott/chaos.html Peckham's List
http://members.tripod.com/~IgorIvanov/physics/nonlinear.html Physics Encyclopedia
http://www.maths.ex.ac.uk/~hinke/dss/index.html Osinga's Software List
Dynamical Systems
http://www.math.sunysb.edu/dynamics/ Dynamical Systems Home Page
http://www.math.psu.edu/gunesch/entropy.html Entropy and Dynamics
Chaos sites
http://www.industrialstreet.net/chaosmetalink/ Chaos Metalink
http://bofh.priv.at/ifs/ Iterated Function Systems Playground
http://www.xahlee.org/PageTwo_dir/more.html Xah Lee's dynamics and Fractals pages
http://acl2.physics.gatech.edu/tutorial/outline.htm Tutorial on Control of Chaos
http://www.mathsoft.com/mathresources/constants/wellknown/article/0,,2090,00.html
All about Feigenbaum Constants
http://www.stud.ntnu.no/~berland/math/feigenbaum/ The Feigenbaum Fractal
http://members.aol.com/MTRw3/index.html Mike Rosenstein's Chaos Page.
http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/cspls.html Chaos in Psychology
http://www.eie.polyu.edu.hk/~cktse/NSR/ Movies and Demonstrations
Time Series
http://www.drchaos.net/drchaos/refs.html Dynamics and Time Series
http://astro.uni-tuebingen.de/groups/time/ Time series Analysis
http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/index.htm
Time Series Data Library
Complex Systems Sites
http://www.math.upatras.gr/~mboudour/nonlin.html Complexity Home Page
http://www.calresco.org/ The Complexity & Artificial Life Web Site
http://www.physionet.org/ Complexity and Physiology Site
Fractals Sites
http://forum.swarthmore.edu/advanced/robertd/index.html#frac A Fractal Gallery
http://spanky.triumf.ca/www/welcome1.html The Spanky Fractal DataBase
http://sprott.physics.wisc.edu/fractals.htm Sprott's Fractal Gallery
http://fractales.inria.fr/ Projet Fractales
http://force.stwing.upenn.edu/~lau/fractal.html Lau's Fractal Stuff
http://skal.planet-d.net/quat/f_gal.html 3D Fractals
http://www.cnam.fr/fractals.html Fractal Gallery
http://www.fractaldomains.com/ Fractal Domains Gallery
http://home1.swipnet.se/~w-17723/fracpro.html Fractal Programs
http://xahlee.org/PageTwo_dir/MathPrograms_dir/mathPrograms.html#Fractals
Fractal Programs
[5] Computational Resources
[5.1] What are general computational resources?
CAIN Europe Archives
http://www.can.nl/education/material/software.html Software Area
FAQ guide to packages from sci.math.num-analysis
ftp://rtfm.mit.edu/pub/usenet/news.answers/num-analysis/faq/part1
NIST Guide to Available Mathematical Software
http://gams.cam.nist.gov/
Mathematics Archives Software
http://archives.math.utk.edu/software.html
Matpack, C++ numerical methods and data analysis library
http://www.matpack.de/
Numerical Recipes Home Page
http://www.nr.com/
[5.2] Where can I find specialized programs for nonlinear
science?
The Academic Software Library:
Chaos Simulations
Bessoir, T., and A. Wolf, 1990. Demonstrates logistic map, Lyapunov exponents,
billiards in a stadium, sensitive dependence, n-body gravitational motion.
Chaos Data Analyser
A PC program for analyzing time series. By Sprott, J.C. and G. Rowlands.
For more info:http://sprott.physics.wisc.edu/cda.htm
Chaos Demonstrations
A PC program for demonstrating chaos, fractals, cellular automata, and related
nonlinear phenomena. By J. C. Sprott and G. Rowlands.
System: IBM PC or compatible with at least 512K of memory.
Available: The Academic Software Library, (800) 955-TASL. $70.
Chaotic Dynamics Workbench
Performs interactive numerical experiments on systems modeled by ordinary
differential equations, including: four versions of driven Duffing
oscillators, pendulum, Lorenz, driven Van der Pol osc., driven Brusselator,
and the Henon-Heils system. By R. Rollins.
System: IBM PC or compatible, 512 KB memory.
Available: The Academic Software Library, (800) 955-TASL, $70
Applied Chaos Tools
Software package for time series analysis based on the UCSD group's, work.
This package is a companion for Abarbanel's book Analysis of Observed Chaotic
Data, Springer-Verlag.
System: Unix-Motif, Windows 95/NT
For more info see: http://www.zweb.com/apnonlin/csp.html
AUTO
Bifurcation/Continuation Software (THE standard). The latest version is
AUTO97. The GUI requires X and Motif to be present. There is also a command
line version AUTO86. The software is transported as a compressed file called
auto.tar.Z.
System: versions to run under X windows--SUN or sgi or LINUX
Available: anonymous ftp from ftp://ftp.cs.concordia.ca/pub/doedel/auto
BZphase
Models Belousov- Zhabotinsky reaction based on the scheme of Ruoff and Noyes.
The dynamics ranges from simple quasisinusoidal oscillations to quasiperiodic,
bursting, complex periodic and chaotic.
System: DOS 6 and higher + PMODE/W DOS Extender. Also openGL version
Available: http://members.tripod.com/~RedAndr/BZPhase.htm
Chaos
Visual simulation in two- and three-dimensional phase space; based on visual
algorithms rather than canned numerical algorithms; well-suited for
educational use; comes with tutorial exercises. By Bruce Stewart
System: Silicon Graphics workstations, IBM RISC workstations with GL
Available: http://msg.das.bnl.gov/~bstewart/software.html
Chaos
A Program Collection for the PC by Korsch, H.J. and H-J. Jodl, 1994, A
book/disk combo that gives a hands-on, computer experiment approach to
learning nonlinear dynamics. Some of the modules cover billiard systems,
double pendulum, Duffing oscillator, 1D iterative maps, an "electronic chaos-
generator", the Mandelbrot set, and ODEs.
System: IBM PC or compatible.
Available: $$http://www.springer-ny.com/catalog/np/updates/0-387-57457-3.html
CHAOS II
Chaos Programs to go with Baker, G. L. and J. P. Gollub (1990) Chaotic
Dynamics. Cambridge, Cambridge Univ.
http://www.cup.org/titles/catalogue.asp?isbn=0521471060
System: IBM, 512K memory, CGA or EGA graphics, True Basic
For more info: contact Gregory Baker, P.O. Box 278 ,Bryn Athyn, PA, 19009
Chaos Analyser
Programs to Time delay embedding, Attractor (3d) viewing and animation,
Poincaré sections, Mutual information, Singular Value Decomposition embedding,
Full Lyapunov spectra (with noise cancellation), Local SVD analysis (for
determining the systems dimension). By Mike Banbrook.
System: Unix, X windows
For more info: http://www.ee.ed.ac.uk/~mb/analysis_progs.html
Chaos Cookbook
These programs go with J. Pritchard's book, The Chaos Cookbook System:
Programs written in Visual Basic & Turbo Pascal
Available: $$http://www.amazon.com/exec/obidos/ASIN/0750617772
Chaos Plot
ChaosPlot is a simple program which plots the chaotic behavior of a damped,
driven anharmonic oscillator.
System: Macintosh
For more info:
http://archives.math.utk.edu/software/mac/diffEquations/.directory.html
Cubic Oscillator Explorer
The CUBIC OSCILLATOR EXPLORER is a Macintosh application which allows
interactive exploration of the chaotic processes of the Cubic Oscillator,
i.e..Duffing's equation.
System: Macintosh + Digidesign DSP card, Digisystem init 2.6 and (optional)
MIDI Manager
Available: (Missing??) Fractal Music
DataPlore
Signal and time series analysis package. Contains standard facilities for
signal processing as well as advanced features like wavelet techniques and
methods of nonlinear dynamics.
Systems: MS Windows, Linux, SUN Solaris 2.6
Available: $$http://www.datan.de/dataplore/
dstool
Free software from Guckenheimer's group at Cornell; DSTool has lots of
examples of chaotic systems, Poincaré sections, bifurcation diagrams.
System: Unix, X windows.
Available: ftp://cam.cornell.edu/pub/dstool/
Dynamical Software Pro
Analyze non-linear dynamics and chaos. Includes ODEs, delay differential
equations, discrete maps, numerical integration, time series embedding, etc.
System: DOS. Microsoft Fortran compiler for user defined equations.
Available: SciTech http://www.scitechint.com/
Dynamics: Numerical Explorations.
A book + disk by H. Nusse, and J.Yorke. A hands on approach to learning the
concepts and the many aspects in computing relevant quantities in chaos
System: PC-compatible computer or X-windows system on Unix computers
Available: $$ http://www.springer-ny.com/detail.tpl?isbn=0387982647
Dynamics Solver
Dynamics Solver solve numerically both initial-value problems and boundary-
value problems for continuous and discrete dynamical systems.
System: Windows 3.1 or Windows 95/98/NT
Available: http://tp.lc.ehu.es/jma/ds/ds.html
DynaSys
Phase plane portraits of 2D ODEs by Etienne Dupuis
System: Windows 95/98
Available: (Missing??)
FD3
A program to estimate fractal dimensions of a set. By DiFalco/Sarraille
System: C source code, suitable for compiling for use on a Unix or DOS
platform.
Available: ftp://ftp.cs.csustan.edu/pub/fd3/
FracGen
FracGen is a freeware program to create fractal images using Iterated
Function Systems. A tutorial is provided with the program. By Patrick Bangert
System: PC-compatible computer, Windows 3.1
Available: http://212.201.48.1/pbangert/site/fracgen.html
Fractal Domains
Generates of Mandelbrot and Julia sets. By Dennis C. De Mars
System: Power Macintosh
Available: http://www.fractaldomains.com/
Fractal Explorer
Generates Mandelbrot and Newton's method fractals. By Peter Stone
System: Power Macintosh
Available: http://usrwww.mpx.com.au/~peterstone/index.html
GNU Plotutils
The GNU plotutils package contains C/C++ function library for exporting 2-D
vector graphics in many file formats, and for doing vector graphics
animations. The package also contains several command-line programs for
plotting scientific data, such as GNU graph, which is based on libplot, and
ODE integration software.
System: GNU/Linux, FreeBSD, and Unix systems.
Available: http://www.gnu.org/software/plotutils/plotutils.html
Ilya
A program to visually study a reaction-diffusion model based on the
Brusselator from Future Skills Software, Herber Sauro.
System: Requires Windows 95, at least 256 colours
Available : http://www.fssc.demon.co.uk/rdiffusion/ilya.htm
INSITE
(It's a Nonlinear Systems Investigative Toolkit for Everyone) is a collection
for the simulation and characterization of dynamical systems, with an emphasis
on chaotic systems. Companion software for T.S. Parker and L.O. Chua (1989)
Practical Numerical Algorithms for Chaotic Systems Springer Verlag. See their
paper "INSITE A Software Toolkit for the Analysis of Nonlinear Dynamical
Systems," Proc. of the IEEE, 75, 1081-1089 (1987).
System: C codes in Unix Tar or DOS format (later requires QuickWindowC
or MetaWINDOW/Plus 3.7C. and MS C compiler 5.1)
Available: INSITE SOFTWARE, p.o. Box 9662, Berkeley, CA , U.S.A.
Institut fur ComputerGraphik
A collection of programs for developing advanced visualization techniques in
the field of three-dimensional dynamical systems. By Löffelmann H., Gröller E.
System: various, requires AVS
Available: http://www.cg.tuwien.ac.at/research/vis/dynsys/
KAOS1D
A tool for studying one-dimensional (1D) discrete dynamical systems. Does
bifurcation diagrams, etc. for a number of maps
System: PC compatible computer, DOS, VGA graphics
Available: http://www.if.ufrgs.br/~arenzon/jsoftw.html
LOCBIF
An interactive tool for bifurcation analysis of non-linear ordinary
differential equations ODE's and maps. By Khibnik, Nikolaev, Kuznetsov and V.
Levitin
System: Now part of XPP (See below)
Available: http://www.math.pitt.edu/~bard/classes/wppdoc/locbif.html
Lyapunov Exponents
Keith Briggs Fortran codes for Lyapunov exponents
System: any with a Fortran compiler
Available: http://more.btexact.com/people/briggsk2/
Lyapunov Exponents and Time Series
Based on Alan Wolf's algorithm, see [2.11], but a more efficient version.
System: Comes as C source, Fortran source, PC executable, etc
Available: http://www.cooper.edu/engineering/physics/wolf/ (Seems to be
missing?)
Lyapunov Exponents and Time Series
Michael Banbrook's C codes for Lyapunov exponents & time series analysis
System: Sun with X windows.
Available: http://www.see.ed.ac.uk/~mb/analysis_progs.html
Lyapunov Exponents Toolbox (LET)
A user-contributed MATLAB toolbox that provides a graphical user interface
for users to determine the full sets of Lyapunov exponents and Lyapunov
dimensions of discrete and continuous chaotic systems.
System: MATLAB 5
Available: ftp://ftp.mathworks.com/pub/contrib/v5/misc/let
Lyapunov.m
A Matlab program based on the QR Method , by von Bremen, Udwadia, and
Proskurowski, Physica D, vol. 101, 1-16, (1997)
System: Matlab
Available: http://www.usc.edu/dept/engineering/mecheng/DynCon/
Macintosh Dynamics Programs
Lists available at: http://hypertextbook.com/chaos/92.shtml
and http://www.xahlee.org/PageTwo_dir/MathPrograms_dir/mathPrograms.html
MacMath
Comes on a disk with the book MacMath, by Hubbard and West. A collection of
programs for dynamical systems (1 & 2 D maps, 1 to 3D flows). Version 9.2 is
the current version, but West is working on a much improved update.
System: Macintosh
For more info: http://www.math.hmc.edu/codee/solvers/mac-math.html
Available: $$ Springer-Verlag http://www.springer-
ny.com/detail.tpl?isbn=0387941355
Madonna
Solves Differential and Difference Equations. Runs STELLA. Has a parser with a
control language. By Robert Macey and George Oster at Berkeley
System: Macintosh or Windows 95 or later
Available : $$ http://www.berkeleymadonna.com/
MatLab Chaos
A collection of routines for generate diagrams which illustrate chaotic
behavior associated with the logistic equation.
System: Requires MatLab.
Available : ftp://ftp.mathworks.com/pub/contrib/misc/chaos/
MTRChaos
MTRCHAOS and MTRLYAP compute correlation dimension and largest Lyapunov
exponents, delay portraits. By Mike Rosenstein.
System: PC-compatible computer running DOS 3.1 or higher, 640K RAM, and EGA
display. VGA & coprocessor recommended
Available: ftp://spanky.triumf.ca/pub/fractals/programs/ibmpc/
Nonlinear Dynamics Toolbox
Josh Reiss' NDT includes routines for the analysis of chaotic data, such as
power spectral analyses, determination of the Lyapunov spectrum, mutual
information function, prediction, noise reduction, and dimensional analysis.
System: Windows 95, 98, or NT
Available : Missing??
NLD Toolbox
This toolbox has many of the standard dynamical systems, By Jeff Brush
System: PC, MS-DOS.
Available: http://www.physik.tu-darmstadt.de/nlp/nldtools/nldtools.html
ODECalc
A program for integrating boundary value and initial value Problems for up to
9th order ODEs. By Optimal Designs.
System: PC 386+, DOS 3.3+, 16 bit arch.
Available : ftp://ftp.mecheng.asme.org/pub/EDU_TOOL/Ode200.exe
PHASER
Kocak, H., 1989. Differential and Difference Equations through Computer
Experiments: with a supplementary diskette containing PHASER: An
Animator/Simulator for Dynamical Systems. Demonstrates a large number of 1D-4D
differential equations--many not chaotic--and 1D-3D difference equations.
System: PC-compatible
Available: Springer-Verlag http://www.springer-
ny.com/detail.tpl?isbn=0387142029
PhysioToolkit
Software for physiologic signal processing and analysis, detection of
physiologically significant events using both classical techniques and novel
methods based on statistical physics and nonlinear dynamics
System: Unix
Available: http://www.physionet.org/physiotools/
Recurrence Quantification Analysis
Recurrence plots give a visual indication of deterministic behavior in complex
time series. The program, by Webber and Zbilut creates the plots and
quantifies the determinism with five measures.
System: DOS executable
Available:http://homepages.luc.edu/~cwebber/
SciLab
A simulation program similar in intent to MatLab. It's primarily designed for
systems/signals work, and is large. From INRIA in France.
Section 3 of 4 - Prev - Next
All sections - 1 - 2 - 3 - 4
| Back to category sci - Use Smart Search |
| Home - Smart Search - About the project - Feedback |
© allanswers.org | Terms of use