TY  - JOUR
AU  - Böttcher, Philipp
AU  - Schäfer, Benjamin
AU  - Kettemann, Stefan
AU  - Agert, Carsten
AU  - Witthaut, Dirk
TI  - Local versus global stability in dynamical systems with consecutive Hopf bifurcations
JO  - Physical review research
VL  - 5
IS  - 3
SN  - 2643-1564
CY  - College Park, MD
PB  - APS
M1  - FZJ-2023-05379
SP  - 033139
PY  - 2023
AB  - 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.
LB  - PUB:(DE-HGF)16
DO  - DOI:10.1103/PhysRevResearch.5.033139
UR  - https://juser.fz-juelich.de/record/1019422
ER  -