  We describe the algorithms used in the Matlab continuation and bifurcation
package pde2path for Hopf bifurcation and continuation of branches of periodic
orbits in systems of PDEs in 1, 2, and 3 spatial dimensions, including the
computation of Floquet multipliers. We first test the methods on three reaction
diffusion examples, namely a complex Ginzburg-Landau equation as a toy problem,
a reaction diffusion system on a disk with rotational waves including stable
(anti) spirals bifurcating out of the trivial solution, and a Brusselator
system with interaction of Turing and Turing-Hopf bifurcations. Then we
consider a system from distributed optimal control, which is ill-posed as an
initial value problem and thus needs a particularly stable method for computing
Floquet multipliers, for which we use a periodic Schur decomposition. The
implementation details how to use pde2path on these problems are given in an
accompanying tutorial, which, together with all other downloads (function
libraries, demos and further documentation) can be found at
http://www.staff.uni-oldenburg.de/hannes.uecker/pde2path.
