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Local versus global stability in dynamical systems with consecutive Hopf bifurcations

Böttcher, Philipp C.; Schäfer, Benjamin ORCID iD icon 1; Kettemann, Stefan; Agert, Carsten; Witthaut, Dirk
1 Institut für Automation und angewandte Informatik (IAI), Karlsruher Institut für Technologie (KIT)

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.


Verlagsausgabe §
DOI: 10.5445/IR/1000165067
Veröffentlicht am 29.11.2023
Originalveröffentlichung
DOI: 10.1103/PhysRevResearch.5.033139
Scopus
Zitationen: 1
Dimensions
Zitationen: 1
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Automation und angewandte Informatik (IAI)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 08.2023
Sprache Englisch
Identifikator ISSN: 2643-1564
KITopen-ID: 1000165067
HGF-Programm 37.12.02 (POF IV, LK 01) Design,Operation & Digitalization of the Future Energy Grids
Weitere HGF-Programme 46.21.04 (POF IV, LK 01) HAICU
Erschienen in Physical Review Research
Verlag American Physical Society (APS)
Band 5
Heft 3
Seiten Art-Nr.: 033139
Vorab online veröffentlicht am 29.08.2023
Nachgewiesen in Dimensions
Scopus
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