Original software packages

AUTO

AUTO can do a limited bifurcation analysis of algebraic systems, systems of ordinary differential equation (ODEs) and it can do certain stationary solution and wave calculations for the partial differential equation (PDE). The latest version is AUTO2000.
available: < http://indy.cs.concordia.ca/auto>

Chaos Data Analyser

Chaos Data Analyzer is a research and teaching tool. When chaos is found, calculations such as the probability distribution, power spectrum, Lyapunov exponent, and various measures of the fractal dimension enable you to determine properties of the system underlying the behavior.
available: < http://sprott.physics.wisc.edu/cda.htm>

DataPlore

Possible fields of use include the analysis of biological and physiological systems, mechanical vibrations, electromagnetic signals, epidemiological studies, time series in geology, finance, economy and many others.
available: < http://www.datan.de/dataplore/>

DsTool

Free software from Guckenheimer's group at Cornell. DsTool is a computational package for analyzing either continuous or discrete dynamical systems and incorporating a user-friendly graphical interface. The user can construct their dynamical system working directly with C source code or through a parser interface which interprets a text description of the dynamical system. The latest version uses a Tcl/Tk interface and is easily installed under different Unix platforms, including Linux. The last version also provides 3D viewing.
available: < http://mathlab.cit.cornell.edu/dyn_sys/dstool/dstool.html >

Dynamics: Numerical Exploration

A book + disk by H. Nusse and J. Yorke. The Dynamics program and handbook allows the reader to explore nonlinear dynamics and chaos by the use of illustrated graphics.
available: <http://www.springer-ny.com/detail.tpl?cart=10596509017979163&ISBN=0387982647>

Dynamics Solver

Dynamics Solver solves numerically both initial-value problems and boundary-value problems for continuous and discrete dynamical systems
available: < http://tp.lc.ehu.es/jma/ds/ds.html>

FD3

A program to estimate fractal dimensions of a set. By DiFalco/Sarraille.
available: < ftp://ftp.cs.csustan.edu/pub/fd3>

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 the paper T.S. Parker and L.O. Chua (1987) "INSITE- A Software Toolkit for the Analysis of Nonlinear Dynamical Systems," Proc. of the IEEE, 75, 1081-1089.
available: < INSITE SOFTWARE, p.o. Box 9662, Berkeley, CA, U.S.A. >

Lyapunov Exponents

K. Briggs Fortran codes for Lyapunov exponents.
available: < http://www.labs.bt.com/people/briggsk2/>

Chaos analysis software

Michael Banbrook's C-codes for Lyapunov exponents and more.
available: < http://www.ee.ed.ac.uk/~mb/analysis_progs.html>

Lyapunov.m

A Matlab program based on the QR Method, by von BRemen, Udwadia and Proskurowski.
available: <http://www.usc.edu/dept/engineering/mecheng/DynCon/>

MTRChaos

MTRCHAOS and MTRLYAP compute correlation dimension and largest Lyapunov exponents, delay portraits. By Mike Rosenstein.
available: <http://spanky.triumf.ca/pub/fractals/PROGRAMS/IBMPC/MTRCHAOS.TXT>

PHASER

A book + disc by H. Kocak. Phaser is a sophisticated program for IBM personal computers, which enables users to experiment with differential and difference equations and dynamical systems in an interactive environment using graphics.
available: <http://www.amazon.de/exec/obidos/ASIN/3540969187/brdnet06/302-6259827-2909622>

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.
available: <http://www.physionet.org/physiotools/>

SciLab

A simulation program similar in intent to MatLab. It's primarily designed for systems/signals work, and is large. From INRIA in France.
available: < ftp://ftp.inria.fr/INRIA/Projects/Meta2/Scilab>

StdMap

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.
available: <http://amath.colorado.edu/faculty/jdm/stdmap.html>

STELLA

Simulates dynamics for Biological and Social systems modelling. Uses a building block metaphor constructing models.
available: <http://www.hps-inc.com/stellavpsr.htm>

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 and Abarbanel.
available: <ftp://lyapunov.ucsd.edu/pub/nonlinear/mbkall>

TISEAN Time Series Analysis

Algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing.
available: <http://www.mpipks-dresden.mpg.de/~tisean/>

XPP-Aut

XPP (XPPAUT is another name; I will use the two interchangeably) is a tool for solving differential equations, difference equations, delay equations, functional equations, boundary value problems, and stochastic equations.
available: <http://www.math.pitt.edu/~bard/xpp/xpp.html>

Matlab packages

DDE-BIFTOOL

DDE-BIFTOOL is a Matlab package for numerical bifurcation analysis of delay differential equations with several fixed discrete and/or state-dependent delays. It allows the computation, continuation and stability analysis of steady state solutions, their Hopf and fold bifurcations, periodic solutions and connecting orbits (but the latter only for the constant delay case). Stability analysis of steady state solutions is achieved through computing approximations and corrections to the rightmost characteristic roots. Periodic solutions, their Floquet multipliers and connecting orbits are computed using piecewise polynomial collocation on adapted meshes.
available: <http://www.cs.kuleuven.ac.be/~koen/delay/ddebiftool.shtml>

Lyapunov Exponents Toolbox (LET)

A user-contribed 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.
available: <ftp://ftp.mathworks.com/pub/contrib/v5/misc/let>