Time-Delay Feedback Control of an Oscillatory Medium

  • 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.

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Metadaten
Author details:Michael Stich, Carsten BetaORCiDGND
DOI:https://doi.org/10.1007/978-3-030-16585-7_1
ISBN:978-3-030-16585-7
ISBN:978-3-030-16584-0
ISSN:2199-3041
ISSN:2199-305X
Title of parent work (English):Biological Systems: Nonlinear Dynamics Approach
Publisher:Springer
Place of publishing:Cham
Publication type:Other
Language:English
Year of first publication:2019
Completion year:2019
Release date:2021/05/03
Volume:20
Page number:17
First page:1
Last Page:17
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert