2017-08-07Zeitschriftenartikel DOI: 10.1088/1367-2630/aa7b61
Timing of transients: quantifying reaching times and transient behavior in complex systems
 dc.contributor.author Kittel, Tim dc.contributor.author Heitzig, Jobst dc.contributor.author Webster, Kevin dc.contributor.author Kurths, Jürgen dc.date.accessioned 2022-03-25T10:32:23Z dc.date.available 2022-03-25T10:32:23Z dc.date.issued 2017-08-07 none dc.date.updated 2022-02-11T07:15:17Z dc.identifier.uri http://edoc.hu-berlin.de/18452/25029 dc.description.abstract In dynamical systems, one may ask how long it takes for a trajectory to reach the attractor, i.e. how long it spends in the transient phase. Although for a single trajectory the mathematically precise answer may be infinity, it still makes sense to compare different trajectories and quantify which of them approaches the attractor earlier. In this article, we categorize several problems of quantifying such transient times. To treat them, we propose two metrics, area under distance curve and regularized reaching time, that capture two complementary aspects of transient dynamics. The first, area under distance curve, is the distance of the trajectory to the attractor integrated over time. It measures which trajectories are ‘reluctant’, i.e. stay distant from the attractor for long, or ‘eager’ to approach it right away. Regularized reaching time, on the other hand, quantifies the additional time (positive or negative) that a trajectory starting at a chosen initial condition needs to approach the attractor as compared to some reference trajectory. A positive or negative value means that it approaches the attractor by this much ‘earlier’ or ‘later’ than the reference, respectively. We demonstrated their substantial potential for application with multiple paradigmatic examples uncovering new features. eng dc.description.sponsorship Deutsche Forschungsgemeinschafthttps://doi.org/10.13039/501100001659 dc.language.iso eng none dc.publisher Humboldt-Universität zu Berlin dc.rights (CC BY 3.0) Attribution 3.0 Unported ger dc.rights.uri https://creativecommons.org/licenses/by/3.0/ dc.subject early-warning signals eng dc.subject complex systems eng dc.subject nonlinear dynamics eng dc.subject ordinary differential equations eng dc.subject stability against shocks eng dc.subject.ddc 530 Physik none dc.title Timing of transients: quantifying reaching times and transient behavior in complex systems none dc.type article dc.identifier.urn urn:nbn:de:kobv:11-110-18452/25029-4 dc.identifier.doi 10.1088/1367-2630/aa7b61 none dc.identifier.doi http://dx.doi.org/10.18452/24376 dc.type.version publishedVersion none local.edoc.container-title New journal of physics : the open-access journal for physics none local.edoc.pages 14 none local.edoc.type-name Zeitschriftenartikel local.edoc.institution Mathematisch-Naturwissenschaftliche Fakultät none local.edoc.container-type periodical local.edoc.container-type-name Zeitschrift local.edoc.container-publisher-name IOP none local.edoc.container-publisher-place [London] none local.edoc.container-volume 19 none local.edoc.container-issue 8 none dc.description.version Peer Reviewed none local.edoc.container-articlenumber 083005 none dc.identifier.eissn 1367-2630