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Determining the sub-Lyapunov exponent of delay systems from time series

AuthorsJüngling, Thomas; Soriano, Miguel C. ; Fischer, Ingo
Issue Date9-Jun-2015
CitationPhysical Review E 91(6): 062908 (2015)
Abstract© 2015 American Physical Society. 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)1063-651X10.1103/PhysRevE.56.5183]. 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.
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevE.91.062908
Identifierse-issn: 1550-2376
issn: 1539-3755
Appears in Collections:(IFISC) Artículos
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