title: Influence of stable Floquet exponents on time-delayed feedback control
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 Rossler 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.
authors.affiliation: School of Mathematical Sciences, Queen Mary & Westfield College, London, United Kingdom. W.Just@qmw.ac.uk
authors.initials: W
authors.lastname: Just
authors.initials: E
authors.lastname: Reibold
authors.initials: K
authors.lastname: Kacperski
authors.initials: P
authors.lastname: Fronczak
authors.initials: JA
authors.lastname: Holyst
authors.initials: H
authors.lastname: Benner