Control of dynamic Hopf bifurcations

1999/03/31 by Nils Berglund
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #chao-dyn #math.OC #nlin.CD #stochastic dynamics and bifurcation

paper · pdf · doi:10.1088/0951-7715/13/1/311

published as Nonlinearity 13:225-248 (2000) · 25 pages, 4 figures

arxiv created 1999/03/31 · openalex publication_date 1999/12/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

The slow passage through a Hopf bifurcation leads to the delayed appearance of large-amplitude oscillations. We construct a smooth scalar feedback control which suppresses the delay and causes the system to follow a stable equilibrium branch. This feature can be used to detect in time the loss of stability of an ageing device. As a by-product, we obtain results on the slow passage through a bifurcation with double-zero eigenvalue, described by a singularly perturbed cubic Liénard equation.

Citations

• Memory effects and scaling laws in slowly driven systems
• Deterministic Nonperiodic Flow

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