Influence of stable Floquet exponents on time-delayed feedback control

Wolfram Just , Ekkehard Reibold , Krzysztof Kacperski , Piotr Fronczak , Janusz Hołyst , Hartmut Benner

Abstract

The performance of time-delayed feedback control is studied by linear stability analysis. Analytical approximations for the resulting eigenvalue spectrum are proposed. Our investigations demonstrate that eigenbranches that develop from the stable Lyapunov exponents of the free system also have a strong influence on the control properties, either by hybridization or by a crossing of branches which interchanges the role of the leading eigenvalue. Our findings are confirmed by numerical analysis of two particular examples, the Toda and the Rössler models. More important is the verification by actual electronic circuit experiments. Here, the observed reduction of control domains can be attributed to these additional eigenvalue branches. The investigations lead to a thorough analytical understanding of the stability properties in time-delayed feedback systems.
Author Wolfram Just - [Queen Mary, University of London]
Wolfram Just,,
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, Ekkehard Reibold - [Technische Universität Darmstadt]
Ekkehard Reibold,,
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, Krzysztof Kacperski (FEIT / IT)
Krzysztof Kacperski,,
- The Institute of Telecommunications
, Piotr Fronczak (FP / PCSD)
Piotr Fronczak,,
- Physics of Complex Systems Divison
, Janusz Hołyst (FP)
Janusz Hołyst,,
- Faculty of Physics
, Hartmut Benner - [Technische Universität Darmstadt]
Hartmut Benner,,
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Journal seriesPhysical Review E, ISSN 1539-3755
Issue year2000
Vol61
No5
Pages5045-5056
ASJC Classification3104 Condensed Matter Physics; 2613 Statistics and Probability; 3109 Statistical and Nonlinear Physics
DOIDOI:10.1103/PhysRevE.61.5045
URL http://link.aps.org/doi/10.1103/PhysRevE.61.5045
Score (nominal)35
Score sourcejournalList
Publication indicators Scopus Citations = 47; WoS Citations = 39; GS Citations = 65.0; Scopus SNIP (Source Normalised Impact per Paper): 2014 = 1.123; WoS Impact Factor: 2006 = 2.438 (2) - 2007=2.484 (5)
Citation count*66 (2020-09-01)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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