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.…
Author details: | Antonio PolitiORCiDGND, Arkadij PikovskijORCiDGND, Ekkehard UllnerORCiDGND |
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URN: | urn:nbn:de:kobv:517-opus4-429790 |
DOI: | https://doi.org/10.25932/publishup-42979 |
ISSN: | 1866-8372 |
Title of parent work (German): | Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (721) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2019/06/12 |
Publication year: | 2017 |
Publishing institution: | Universität Potsdam |
Release date: | 2019/06/12 |
Tag: | networks |
Issue: | 721 |
Number of pages: | 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 |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access |
License (German): | CC-BY - Namensnennung 4.0 International |