title: Determining the sub-Lyapunov exponent of delay systems from time series.
abstract: For delay systems the sign of the sub-Lyapunov exponent (sub-LE) determines key dynamical properties. This includes the properties of strong and weak chaos and of consistency. Here we present a robust algorithm based on reconstruction of the local linearized equations of motion, which allows for calculating the sub-LE from time series. The algorithm is inspired by a method introduced by Pyragas for a nondelayed drive-response scheme [K. Pyragas, Phys. Rev. E 56, 5183 (1997)]. In the presented extension to delay systems, the delayed feedback takes over the role of the drive, whereas the response of the low-dimensional node leads to the sub-Lyapunov exponent. Our method is based on a low-dimensional representation of the delay system. We introduce the basic algorithm for a discrete scalar map, extend the concept to scalar continuous delay systems, and give an outlook to the case of a full vector-state system, from which only a scalar observable is recorded.
authors.affiliation: Institute for Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC), Campus University of the Balearic Islands, E-07122 Palma de Mallorca, Spain.
authors.forename: Thomas
authors.initials: T
authors.lastname: Jüngling
authors.affiliation: Institute for Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC), Campus University of the Balearic Islands, E-07122 Palma de Mallorca, Spain.
authors.forename: Miguel C
authors.initials: MC
authors.lastname: Soriano
authors.affiliation: Institute for Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC), Campus University of the Balearic Islands, E-07122 Palma de Mallorca, Spain.
authors.forename: Ingo
authors.initials: I
authors.lastname: Fischer