Identification and characterization of systems with delayed feedback: (I) Theory and tools

Simple item page
dc.creatorBünner, Martin J.
dc.creatorCiofini, Marco
dc.creatorGiaquinta, Antonino
dc.creatorHegger, Rainer
dc.creatorKantz, Holger
dc.creatorMeucci, Riccardo
dc.creatorPoliti, Antonio
dc.date1999-07-13
dc.date.accessioned2026-07-07T02:35:47Z
dc.date.available2026-07-07T02:35:47Z
dc.descriptionHigh-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems defined on sufficiently high dimensional spaces is thoroughly discussed. The dimension of the ``embedding'' space turns out to be independent of the delay time and thus of the dimensionality of the attractor dynamics. As a consequence, the procedure described in the present paper turns out to be definitely advantageous with respect to the standard ``embedding'' technique in the case of high-dimensional chaos, when the latter is practically unapplicable. The mapping is not exact when delayed maps are used to reproduce the dynamics of time-continuous systems, but the errors can be kept under control. In this context, the approximation of delay-differential equations is discussed with reference to different classes of maps. Appropriate tools to estimate the a priori unknown delay time and the number of hidden components are introduced. The generalized Mackey-Glass system is investigated in detail as a testing ground for the theoretical considerations.
dc.descriptionsubmitted to EPJ
dc.identifierhttps://arxiv.org/abs/chao-dyn/9907020
dc.identifierhttp://arxiv.org/abs/chao-dyn/9907020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/15737
dc.subjectChaotic Dynamics
dc.titleIdentification and characterization of systems with delayed feedback: (I) Theory and tools
dc.typetext

Files

Collections

arXiv