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Chaotic macroscopic phases in one-dimensional oscillators

  • The connection between the macroscopic description of collective chaos and the underlying microscopic dynamics is thoroughly analysed in mean-field models of one-dimensional oscillators. We investigate to what extent infinitesimal perturbations of the microscopic configurations can provide information also on the stability of the corresponding macroscopic phase. In ensembles of identical one-dimensional dynamical units, it is possible to represent the microscopic configurations so as to make transparent their connection with the macroscopic world. As a result, we find evidence of an intermediate, mesoscopic, range of distances, over which the instability is neither controlled by the microscopic equations nor by the macroscopic ones. We examine a whole series of indicators, ranging from the usual microscopic Lyapunov exponents, to the collective ones, including finite-amplitude exponents. A system of pulse-coupled oscillators is also briefly reviewed as an example of non-identical phase oscillators where collective chaos spontaneouslyThe connection between the macroscopic description of collective chaos and the underlying microscopic dynamics is thoroughly analysed in mean-field models of one-dimensional oscillators. We investigate to what extent infinitesimal perturbations of the microscopic configurations can provide information also on the stability of the corresponding macroscopic phase. In ensembles of identical one-dimensional dynamical units, it is possible to represent the microscopic configurations so as to make transparent their connection with the macroscopic world. As a result, we find evidence of an intermediate, mesoscopic, range of distances, over which the instability is neither controlled by the microscopic equations nor by the macroscopic ones. We examine a whole series of indicators, ranging from the usual microscopic Lyapunov exponents, to the collective ones, including finite-amplitude exponents. A system of pulse-coupled oscillators is also briefly reviewed as an example of non-identical phase oscillators where collective chaos spontaneously emerges.show moreshow less

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Metadaten
Author:Antonio PolitiORCiDGND, Arkady PikovskyORCiDGND, Ekkehard UllnerORCiDGND
URN:urn:nbn:de:kobv:517-opus4-429790
DOI:https://doi.org/10.25932/publishup-42979
ISSN:1866-8372
Parent Title (German):Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (721)
Document Type:Postprint
Language:English
Date of first Publication:2019/06/12
Year of Completion:2017
Publishing Institution:Universität Potsdam
Release Date:2019/06/12
Tag:networks
Issue:721
Pagenumber:20
Source:The European Physical Journal Special Topics 226 (2017) 9, S. 1791–1810 DOI: 10.1140/epjst/e2017-70056-4
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Publication Way:Open Access
Licence (German):License LogoCreative Commons - Namensnennung, 4.0 International