title: Reconstruction of time-delay systems from chaotic time series.
abstract: We propose a method that allows one to estimate the parameters of model scalar time-delay differential equations from time series. The method is based on a statistical analysis of time intervals between extrema in the time series. We verify our method by using it for the reconstruction of time-delay differential equations from their chaotic solutions and for modeling experimental systems with delay-induced dynamics from their chaotic time series.
authors.affiliation: Saratov Department of the Institute of RadioEngineering and Electronics of Russian Academy of Sciences, Zelyonaya Street, 38, Saratov, 410019, Russia.
authors.forename: B P
authors.initials: BP
authors.lastname: Bezruchko
authors.forename: A S
authors.initials: AS
authors.lastname: Karavaev
authors.forename: V I
authors.initials: VI
authors.lastname: Ponomarenko
authors.forename: M D
authors.initials: MD
authors.lastname: Prokhorov