Chaotic macroscopic phases in one-dimensional oscillators

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Abstract

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 spontaneously emerges.
Original languageEnglish
Pages (from-to)1791-1810
Number of pages20
JournalThe European Physical Journal. Special Topics
Volume226
Issue number9
Early online date21 Jun 2017
DOIs
Publication statusPublished - Jun 2017

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Chaos theory
oscillators
chaos
exponents
configurations
perturbation
pulses

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Chaotic macroscopic phases in one-dimensional oscillators. / Politi, Antonio; Pikovsky, Arkady ; Ullner, Ekkehard.

In: The European Physical Journal. Special Topics, Vol. 226, No. 9, 06.2017, p. 1791-1810.

Research output: Contribution to journalArticle

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