DSWeb Dynamical Systems Software aims to collect all available software on dynamical systems theory. This project was originally launched during the special year Emerging Applications of Dynamical Systems, 1997/1998, at the Institute for Mathematics and its Applications. The information here includes functionality, platforms, languages, references, and contacts.

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XPP

By Bard Ermentrout
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XPP-Aut, X-Windows Phase Plane plus Auto

XPP (also called XPPAUT) is a tool for solving:

  • differential equations,
  • difference equations,
  • delay equations,
  • functional equations,
  • boundary value problems, and
  • stochastic equations.

XPP contains the code for the popular bifurcation program, AUTO. Thus, you can switch back and forth between XPP and AUTO, using the values of one program in the other and vice-versa. Bard Ermentrout put a "friendly" face on AUTO, so you do not need to know much about it to play around with it.

The online tutorial demonstrates how to use XPP and gives lots of examples. There is also an online help facility.

XPP has the capabilities for handling up to 590 differential equations.

  • There are over a dozen solvers including several for stiff systems, a solver for integral equations and a symplectic solver.
  • Up to 10 graphics windows can be visible at once and a variety of color combinations is supported.
  • PostScript output is supported as well as GIF and animated GIF movies
  • Post processing is easy and includes the ability to make histograms, FFTs and applying functions to columns of your data.
  • Equilibria and linear stability as well as one-dimensional invariant sets can be computed.
  • Nullclines and flow fields aid in the qualitative understanding of two-dimensional models.
  • Poincare maps and equations on cylinders and tori are also supported.
  • Some useful averaging theory tricks and various methods for dealing with coupled oscillators are included.
  • Equations with Dirac delta functions are allowed.
  • There is an animation package that allows you to create animated versions of your simulations, such as a little pendulum moving back and forth or lamprey swimming.
  • There is a curve-fitter based on the Marquardt-Levenberg algorithm which lets you fit data points to the solutions to dynamical systems.
  • It is possible to automatically generate "movies" of three-dimensional views of attractors or parametric changes in an attractor.
  • It is possible to dynamically link to external subroutines.

 


 

KeywordsBifurcation analysis, Continuation, Dynamics (phase diagrams), Visualization
Model
  • Maps
  • ODEs
  • DDEs
Software Type
  • Package
Language
  • C
Platform
  • Unix
  • Linux
  • Windows
  • MacOS
Availability
Free download from website (source and binaries available for several platforms): https://sites.pitt.edu/~phase/bard/bardware/xpp/xpp.html.
Contact Person
References to Papers
Bard Ermentrout
"Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students"
SIAM, 2002
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