Mathematical software

Here is a list, in alphabetical order, of general purpose mathematical software that has the following characteristics:

• They can be used interactively, by typing in commands and/or using a graphical interface
  
   
• Sequences of commands can be stored to file to create scripts, which can then be run as programs
  
   
• They can all plot 2D and 3D graphs, and plot other data.
  
   

AUTO:

The grandparent of packages such as XPPAUT, PyDSTool and MatCont (see below), AUTO is dedicated to generating s using . It has a command line interface in Python, but is probably more easily accessed via one of the other packages. http://indy.cs.concordia.ca/auto/

MatCont:

MatCont is a freely-available MATLAB (see below) software package for analysing dynamical systems using numerical continuation to create bifurcation diagrams. http://sourceforge.net/projects/matcont/

MATLAB:

MATLAB is a commercially available software package designed for numerical computations and data visualisation in science and engineering. MathWorks sell many additional toolboxes, including ones for statistics. There are also many contributed packages available, including a number with neuroscience applications. The graphics are interactive. It is available for Linux, Windows and MacOS. MATLAB is included in this list because of its wide use, even though it is not open source. http://www.mathworks.com/

OCTAVE:

GNU Octave is an open source software environment, primarily intended for numerical computations. Its language is mostly compatible with MATLAB. It includes routines for solving sets of coupled ODEs and optimisation. It is available for Linux, Windows and MacOS. http://www.gnu.org/software/octave/

PyDSTool:

PyDSTool is a developing open source integrated simulation, modelling and analysis package for dynamical systems, based on the SciPy package (see above). As well as solving systems of ODEs, it can be used to create bifurcation diagrams using . http://pydstool.sourceforge.net/

R:

Officially known as the R project for statistical computing, R is an open source software environment designed for statistical computing and graphics, though which can be used as a general purpose mathematical tool. It includes optimisation functions, and there is a wide array of contributed packages, including for solving sets of coupled differential equations. While the graphics capabilities are impressive, it is not possible to use the mouse to interact with plots, e.g. zooming in to a region of the data, though efforts are underway to make this possible. It is available for UNIX platforms, Windows and MacOS. http://www.r-project.org

SciPy:

Short for "Scientific Tools for Python", SciPy is open source software environment for mathematics and science implemented in the Python programming language. The SciPy provides many numerical routines including ones for optimisation. The graphics are interactive. It is available for Linux, Windows and MacOS. http://www.scipy.org

XPPAUT:

General equation solver . Allows easy definition and numerical solution of the systems of ODEs that arise in compartmental modelling. Particularly useful for simulating reduced neuronal models such as Morris-Lecar and Fitzhugh-Nagumo, and examining phase plane plots of cell dynamics. It can also be used to create bifurcation diagrams using . It is available for Linux, Windows and MacOS. http://www.math.pitt.edu/~bard/xpp/xpp.html