Journal Article

FZJ-2023-05379

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Local versus global stability in dynamical systems with consecutive Hopf bifurcations

Böttcher, P. (Corresponding author)FZJ* ; Schäfer, B. ; Kettemann, S. ; Agert, C. ; Witthaut, D.FZJ*

2023
APS College Park, MD

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Please use a persistent id in citations: doi:10.1103/PhysRevResearch.5.033139

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.

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Contributing Institute(s):

1. Modellierung von Energiesystemen (IEK-10)
2. Systemforschung und Technologische Entwicklung (IEK-STE)

Research Program(s):

1. 1122 - Design, Operation and Digitalization of the Future Energy Grids (POF4-112) (POF4-112)
2. CoNDyNet 2 - Kollektive Nichtlineare Dynamik Komplexer Stromnetze (BMBF-03EK3055B) (BMBF-03EK3055B)
3. DFG project 491111487 - Open-Access-Publikationskosten / 2022 - 2024 / Forschungszentrum Jülich (OAPKFZJ) (491111487) (491111487)
4. HGF-ZT-I-0029 - Helmholtz UQ: Uncertainty Quantification - from data to reliable knowledge (HGF-ZT-I-0029) (HGF-ZT-I-0029)
5. 1111 - Effective System Transformation Pathways (POF4-111) (POF4-111)

Appears in the scientific report 2023

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Database coverage:
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