2023/02/16 by Philipp Böttcher, Benjamin Schäfer, Böttcher, Philipp C. +7
Computer Science · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaos control and synchronization #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2302.08566
openalex publication_date 2023/02/16 · openalex created_date 2023/02/21 · openalex updated_date 2026/08/01
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 on these two aspects of stability: Global stability is large close to the point where the system loses its local 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.