Computational Resources
- The Academic Software Library:
Applied Chaos Tools
- 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 infohttp://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
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.
System: IBM PC or compatible, 512 KB
Available: The Academic Software Library, (800) 955-TASL,
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,
System: Unix-Motif, Windows 95/NT
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 fromftp://ftp.cs.concordia.ca/pub/doedel/auto
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
System: DOS 6 and higher + PMODE/W DOS Extender. Also openGL
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
System: Silicon Graphics workstations, IBM RISC workstations
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
- 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/38/052138897X.html
System: IBM, 512K memory, CGA or EGA graphics, True Basic
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, Poincar sections, Mutual information, Singular Value
Decomposition embedding, Full Lyapunov spectra (with noise cancellation), Local
SVD analysis (for determining the systems dimension). By Mike
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
- Chaos Plot
ChaosPlot is a simple program which plots the chaotic
behavior of a damped, driven anharmonic oscillator.
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.
Macintosh + Digidesign DSP card, Digisystem init 2.6 and (optional) MIDI
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.
Windows, Linux, SUN Solaris 2.6
Free software from Guckenheimer's group at Cornell;
DSTool has lots of examples of chaotic systems, Poincar sections, bifurcation
System: Unix, X windows.
- 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.
- 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
computer or X-windows system on Unix computers
- Dynamics Solver
Dynamics Solver solve numerically both
initial-value problems and boundary-value problems for continuous and discrete
System: Windows 3.1 or Windows
Phase plane portraits of 2D ODEs by Etienne
System: Windows 95/98
A program to estimate fractal dimensions of a set. By
System: C source code, suitable for compiling for
use on a Unix or DOS platform.
FracGen is a freeware program to create fractal images
using Iterated Function Systems. A tutorial is provided with the program. By
System: PC-compatible computer, Windows
- Fractal Domains
Generates of Mandelbrot and Julia sets. By
Dennis C. De Mars
System: Power Macintosh
- Fractal Explorer
Generates Mandelbrot and Newton's method
fractals. By Peter Stone
System: Power Macintosh
- 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.
A program to visually study a reaction-diffusion model
based on the Brusselator from Future Skills Software, Herber
System: Requires Windows 95, at least 256
(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
System: C codes in Unix Tar or DOS format (later requires
or MetaWINDOW/Plus 3.7C. and MS C compiler
Available: INSITE SOFTWARE, p.o. Box 9662, Berkeley, CA ,
- Institut fur ComputerGraphik
A collection of programs for
developing advanced visualization techniques in the field of three-dimensional
dynamical systems. By L[sinvcircumflex]ffelmann H., Gr[sinvcircumflex]ller
System: various, requires AVS
A tool for studying one-dimensional (1D) discrete
dynamical systems. Does bifurcation diagrams, etc. for a number of
System: PC compatible computer, DOS, VGA
An interactive tool for bifurcation analysis of
non-linear ordinary differential equations ODE's and maps. By Khibnik,
Nikolaev, Kuznetsov and V. Levitin
System: DOS version 3.0 or
- Lyapunov Exponents
Keith Briggs Fortran codes for Lyapunov
System: any with a Fortran compiler
- Lyapunov Exponents and Time Series
Based on Alan Wolf's
, but a more efficient version.
System: Comes as C source, Fortran
source, PC executable, etc
- Lyapunov Exponents and Time Series
Michael Banbrook's C codes
for Lyapunov exponents & time series analysis
System: Sun with X
- 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
A Matlab program based on the QR Method , by von
Bremen, Udwadia, and Proskurowski, Physica D, vol. 101, 1-16,
- Macintosh Dynamics Programs
List available at:http://hypertextbook.com/chaos/92.shtml
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
For more info:http://www.math.hmc.edu/codee/solvers/mac-math.html
Available: $$ Springer-Verlaghttp://www.springer-ny.com/math/text_books/de_und.htm
Solves Differential and Difference Equations. Runs
STELLA. Has a parser with a control language.
System: Macintosh or
- MatLab Chaos
A collection of routines for generate diagrams
which illustrate chaotic behavior associated with the logistic
System: Requires MatLab.
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
- 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
- NLD Toolbox
This toolbox has many of the standard dynamical
systems, By Jeff Brush
System: PC, MS-DOS.
A program for integrating boundary value and initial
value Problems for up to 9th order ODEs. By Optimal Designs.
PC 386+, DOS 3.3+, 16 bit arch.
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
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
- 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
A simulation program similar in intent to MatLab. It's
primarily designed for systems/signals work, and is large. From INRIA in
System: Unix, X Windows, 20 Meg Disk
Iterates Area Preserving Maps, by J. D. Meiss. Iterates 8
different maps. It will find periodic orbits, cantori, stable and unstable
manifolds, and allows you to iterate curves.
Simulates dynamics for Biological and Social systems
modelling. Uses a building block metaphor constructing
System: Macintosh and Windows PC
- Time Series Tools
An extensive list of Unix tools for Time
For more info:http://chuchi.df.uba.ar/guille/TS/tools/tools.html
- Time Series Analysis from Darmstadt
Four prgrams Time Series
analysis and Dimension calculation. Three of them look like codes for OS2
(haven't confirmed this), and one is a std Fortran source
For more info:http://www.physik.th-darmstadt.de/nlp/distribution.html
- Time Series Analysis from Kennel
The program mkball finds the
minimum embedding dimension using the false strands enhancement of the false
neighbors algorithm of Kennel & Abarbanel.
System: any C
- TISEAN Time Series Analysis
Agorithms for data
representation, prediction, noise reduction, dimension and Lyapunov estimation,
and nonlinearity testing. By Rainer Hegger, Holger Kantz and Thomas
System: C, C++ and Fortran Codes for
- Tufillaro's Programs
From the book Nonlinear Dynamics and Chaos
by Tufillaro, Abbot and Reilly (1992) (for a sample section seehttp://cnls.lanl.gov/People/nbt/Book/openall3.ps
). A collection of programs for the Macintosh.
For more info:http://cnls.lanl.gov/People/nbt/qm.html
- Unified Life Models (ULM)
ULM, by Stephane Legendre, is a
program to study population dynamics and more generally, discrete dynamical
systems. It models any species life cycle graph (matrix models) inter- and
intra-specific competition (non linear systems), environmental stochasticity,
demographic stochasticity (branching processes), and metapopulations,
migrations (coupled systems).
- Virtual Laboratory
Simulations of 2D active media by the Complex
Systems Group at the Max Planck Inst. in Berlin.
Requires PV-Wave by Visual Numerics $http://www.vni.com/products/wave/$
- VRA (Visual Recurrence Analysis)
VRA is a software to display
and Study the recurrence plots, first described by Eckmann, Oliffson Kamphorst
And Ruelle in 1987. With RP, one can graphically detect hidden patterns and
structural changes in data or see similarities in patterns across the time
series under study. By Eugene Kononov
Phase 3D plane program for X-windows systems (for
systems like Lorenz, Rossler). Plot, rotate in 3-d, Poincar sections, etc. By
Thomas P. Witelski
System: X-windows, Unix, SunOS 4
Differential equations and maps for x-windows systems.
Links to Auto for bifurcation analysis. By Bard Ermentrout
X-windows, Binaries for many unix systems
Simulate pattern formation in 2-D excitable media (in
particular 2 models, one of them the FitzHugh-Nagumo). By Flavio