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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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pde2path

Runner-up - DSWeb 2018 Software Contest

By Hannes Uecker, Jens Rademacher
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pde2path
The software tool pde2path is a Matlab package for numerical continuation and bifurcation analysis of FEM based numerical discretizations for PDE systems on one-, two- or three-dimensional domains, possibly coupled with auxiliary constraint equations. pde2path can be used for the continuation of equilibria, traveling waves and time-periodic solutions. It can detect stationary bifurcations, possibly of higher multiplicity, as well as Hopf bifurcations, and perform a branch switching. Depending on the system type, pde2path also allows for an easy switch between time-simulations and continuation.
KeywordsPDE, bifurcations, numerical continuation
Model
  • PDEs
Software Type
  • Package
Language
  • MatLab
Platform
  • Linux
  • Windows
  • MacOS
Availability
Contact Person
References to Papers
W.J. Beyn and V. Thümmler. Phase conditions, symmetries, and PDE continuation. In Numerical continuation methods for dynamical systems, pages 301–330. Springer, Dordrecht, 2007.
E. Doedel, A. R. Champneys, Th. F. Fairgrieve, Y. A. Kuznetsov, Bj. Sandstede, and X. Wang. AUTO: Continuation and bifurcation software for ordinary differential equations (with HomCont). http://indy.cs.concordia.ca/auto/, 1997.
T. Dohnal, J.D.M. Rademacher, H. Uecker, and D. Wetzel. pde2path 2.0. In H. Ecker, A. Steindl, and S. Jakubek, editors, ENOC 2014 - Proceedings of 8th European Nonlinear Dynamics Conference, ISBN: 978-3-200-03433-4, 2014.
T. Dohnal and H. Uecker. Periodic boundary conditions in pde2path, 2017.
H. de Witt, T. Dohnal, J.D.M. Rademacher, H. Uecker, and D. Wetzel. pde2path - Quickstart guide and reference card, 2018.
S. Engelnkemper, S. V. Gurevich, H. Uecker, D. Wetzel, and U. Thiele. Continuation for thin film hydrodynamics and related scalar problems. In Computational Modeling of Bifurcations and Instabilities in Fluid Mechanics, Computational Methods in Applied Sciences, 50, pages 459–501.
Springer, 2019.
B. Ermentrout. Stripes or spots? Nonlinear effects in bifurcation of reaction-diffusion equations on the square. Proc. R. Soc. Lond., Ser. A, 434(1891):413–417, 1991.
M. Golubitsky and I. Stewart. The symmetry perspective. Birkhäuser, Basel, 2002.
D. Kressner. An efficient and reliable implementation of the periodic qz algorithm. In IFAC Workshop on Periodic Control Systems. 2001.
U. Prüfert. OOPDE, www.mathe.tu-freiberg.de/nmo/mitarbeiter/uwe-pruefert/software,
2016.
J.D.M. Rademacher and H. Uecker. Symmetries, freezing, and Hopf bifurcations of modulated traveling waves in pde2path, 2017.
J.D.M. Rademacher and H. Uecker. The OOPDE setting of pde2path – a tutorial via some Allen-Cahn models, 2018.
H. Uecker. Optimal harvesting and spatial patterns in a semi arid vegetation system. Natural Resource Modelling, 29(2):229–258, 2016.
H. Uecker. Infinite time–horizon spatially distributed optimal control problems with pde2path – a tutorial, 2017.
H. Uecker. User guide on Hopf bifurcation and time periodic orbits with pde2path, 2017.
H. Uecker. Hopf bifurcation and time periodic orbits with pde2path – algorithms and applications, Comm. in Comp. Phys, to appear, 2018.
H. Uecker. Multiple bifurcation points in pde2path, Preprint, 2018.
H. Uecker. Pattern formation with pde2path – a tutorial, 2018.
H. Uecker. www.staff.uni-oldenburg.de/hannes.uecker/pde2path, 2018.
H. Uecker and D. Wetzel. Snaking branches of localized body-centered cubes, in preparation, 2018.
H. Uecker, D. Wetzel, and J.D.M. Rademacher. pde2path – a Matlab package for continuation and bifurcation in 2D elliptic systems. NMTMA, 7:58–106, 2014.

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