Time-delay feedback control of an oscillatory medium

Michael Stich*, Carsten Beta

*Corresponding author for this work

Research output: Chapter in Book/Published conference outputChapter


The supercritical Hopf bifurcation is one of the simplest ways in which a stationary state of a nonlinear system can undergo a transition to stable self-sustained oscillations. At the bifurcation point, a small-amplitude limit cycle is born, which already at onset displays a finite frequency. If we consider a reaction-diffusion system that undergoes a supercritical Hopf bifurcation, its dynamics is described by the complex Ginzburg-Landau equation (CGLE). Here, we study such a system in the parameter regime where the CGLE shows spatio-temporal chaos. We review a type of time-delay feedback methods which is suitable to suppress chaos and replace it by other spatio-temporal solutions such as uniform oscillations, plane waves, standing waves, and the stationary state.

Original languageEnglish
Title of host publicationSEMA SIMAI Springer Series
EditorsJ. Landeira, B. Escribano
Number of pages17
ISBN (Electronic)978-3-030-16585-7
ISBN (Print)978-3-030-16584-0
Publication statusE-pub ahead of print - 30 Apr 2019

Publication series

NameSEMA SIMAI Springer Series
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X


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