Time-delay feedback control of an oscillatory medium

Michael Stich*, Carsten Beta

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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
PublisherSpringer
Pages1-17
Number of pages17
ISBN (Electronic)978-3-030-16585-7
ISBN (Print)978-3-030-16584-0
DOIs
Publication statusE-pub ahead of print - 30 Apr 2019

Publication series

NameSEMA SIMAI Springer Series
Volume20
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X

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  • Cite this

    Stich, M., & Beta, C. (2019). Time-delay feedback control of an oscillatory medium. In J. Landeira, & B. Escribano (Eds.), SEMA SIMAI Springer Series (pp. 1-17). (SEMA SIMAI Springer Series; Vol. 20). Springer. https://doi.org/10.1007/978-3-030-16585-7_1