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@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},
}