% IMPORTANT: The following is UTF-8 encoded. This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.
@ARTICLE{Bttcher:1019422,
author = {Böttcher, Philipp and Schäfer, Benjamin and Kettemann,
Stefan and Agert, Carsten and Witthaut, Dirk},
title = {{L}ocal versus global stability in dynamical systems with
consecutive {H}opf bifurcations},
journal = {Physical review research},
volume = {5},
number = {3},
issn = {2643-1564},
address = {College Park, MD},
publisher = {APS},
reportid = {FZJ-2023-05379},
pages = {033139},
year = {2023},
abstract = {Quantifying the stability of an equilibrium is central in
the theory of dynamical systems as well as in engineering
and control. A comprehensive picture must include the
response to both small and large perturbations, leading to
the concepts of local (linear) and global stability. Here,
we show how systems displaying Hopf bifurcations show
contrarian results for these two aspects of stability:
Global stability is large close to the point where the
system loses its stability altogether. We demonstrate this
effect for an elementary model system, an anharmonic
oscillator, and a realistic model of power system dynamics
with delayed control. Detailed investigations of the
bifurcation explain the seeming paradox in terms of the
location of the attractors relative to the equilibrium.},
cin = {IEK-10 / IEK-STE},
ddc = {530},
cid = {I:(DE-Juel1)IEK-10-20170217 / I:(DE-Juel1)IEK-STE-20101013},
pnm = {1122 - Design, Operation and Digitalization of the Future
Energy Grids (POF4-112) / CoNDyNet 2 - Kollektive
Nichtlineare Dynamik Komplexer Stromnetze (BMBF-03EK3055B) /
DFG project 491111487 - Open-Access-Publikationskosten /
2022 - 2024 / Forschungszentrum Jülich (OAPKFZJ)
(491111487) / HGF-ZT-I-0029 - Helmholtz UQ: Uncertainty
Quantification - from data to reliable knowledge
(HGF-ZT-I-0029) / 1111 - Effective System Transformation
Pathways (POF4-111)},
pid = {G:(DE-HGF)POF4-1122 / G:(DE-JUEL1)BMBF-03EK3055B /
G:(GEPRIS)491111487 / G:(DE-Ds200)HGF-ZT-I-0029 /
G:(DE-HGF)POF4-1111},
typ = {PUB:(DE-HGF)16},
doi = {10.1103/PhysRevResearch.5.033139},
url = {https://juser.fz-juelich.de/record/1019422},
}