@Article{CiCP-25-812,
author = {Hannes Uecker},
title = {Hopf Bifurcation and Time Periodic Orbits with pde2path – Algorithms and Applications},
journal = {Communications in Computational Physics},
year = {2018},
volume = {25},
number = {3},
pages = {812--852},
abstract = {<p style="text-align: justify;">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 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 also includes a number of further examples and algorithms,
for instance on Hopf bifurcation with symmetries, on Hopf point continuation, and on
branch switching from periodic orbits.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0181},
url = {http://global-sci.org/intro/article_detail/cicp/12830.html}
}