Current Hopf library written and maintained by H. Uecker
The hopf library as part of the Matlab package
pde2path (v2.3) provides functions for
continuation of time periodic orbits of the pde2path class
of PDEs. For this it couples the standard pde2path setup
with (modifications of) the BVP solver
TOM.
To run it efficiently we recommend to also download
ilupack ; mex
it, add it to the Matlab path, and then set p.hopf.ilss=1;
before calling p=cont(p,10); on a Hopf branch.
Have a look at the Hopf tutorial,
and the Hopf Algorithms and Applications,
and the m-files in /pdepath/hopfdemos which come with pde2path
for more information. For comparison and reference here we provide some
verbatim outputs of
these demos, and some movies.
A complex Ginzburg-Landau equation. html-publish of the cmds files:
1D,
2D,
3D.
Example movies 2D and 3D (Hopf orbits to (rescaled) spatial wave-vectors k=(2,1) and k=(2,1,1), with Dirichlet BC)
Rotating patterns on a disk. html-publish of the cmds file: rotcmds.
Movie of Hopf orbits (u-component) on 5 Hopf branches, first for alpha=0 (rotcmds_a.m):
For alpha=1 and at larger r=3, many solutions take the form of (anti)spiral waves(rotcmds_b.m):
3D plot; u-component, r=3, alpha=1, delta=0.1:
An extended Brusselator. html-publish of the cmds files:
1D,
2D.
Movie of the Hopf orbit at "s2h1/pt5":
A canonical system for "Optimal pollution".
publish of pollcmds.
To start your own simulations, copy files from a hopfdemo similar to your
system into a new directory, and start modifying these files.
For bugs, questions or remarks please write to: hannes.uecker -- at -- uni-oldenburg.de.
Any feedback is welcome.