Influence of stable Floquet exponents on time-delayed feedback control

Wolfram Just, Ekkehard Reibold, Krzysztof Kacperski, Piotr Fronczak, Janusz A. Hołyst, Hartmut Benner
2000 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
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
more » ... umerical 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. PACS number͑s͒: 05.45.Gg PRE 61 WOLFRAM JUST et al. PRE 61 WOLFRAM JUST et al.
doi:10.1103/physreve.61.5045 pmid:11031547 fatcat:f6bcr53sujdwzkjcwdao6njuq4