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 International Publishing AG
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

Fingerprint

Complex Ginzburg-Landau Equation
Hopf bifurcation
Landau-Ginzburg equations
Stationary States
feedback control
Chaos theory
Hopf Bifurcation
Feedback Control
Feedback control
chaos
oscillation
Time Delay
Time delay
time lag
Oscillation
Spatiotemporal Chaos
oscillations
Standing Wave
Bifurcation Point
nonlinear systems

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 International Publishing AG. https://doi.org/10.1007/978-3-030-16585-7_1
Stich, Michael ; Beta, Carsten. / Time-delay feedback control of an oscillatory medium. SEMA SIMAI Springer Series. editor / J. Landeira ; B. Escribano. Springer International Publishing AG, 2019. pp. 1-17 (SEMA SIMAI Springer Series).
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Stich, M & Beta, C 2019, Time-delay feedback control of an oscillatory medium. in J Landeira & B Escribano (eds), SEMA SIMAI Springer Series. SEMA SIMAI Springer Series, vol. 20, Springer International Publishing AG, pp. 1-17. https://doi.org/10.1007/978-3-030-16585-7_1

Time-delay feedback control of an oscillatory medium. / Stich, Michael; Beta, Carsten.

SEMA SIMAI Springer Series. ed. / J. Landeira; B. Escribano. Springer International Publishing AG, 2019. p. 1-17 (SEMA SIMAI Springer Series; Vol. 20).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Stich M, Beta C. Time-delay feedback control of an oscillatory medium. In Landeira J, Escribano B, editors, SEMA SIMAI Springer Series. Springer International Publishing AG. 2019. p. 1-17. (SEMA SIMAI Springer Series). https://doi.org/10.1007/978-3-030-16585-7_1