Chaotic macroscopic phases in one-dimensional oscillators

Antonio Politi, Arkady Pikovsky, Ekkehard Ullner

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
12 Downloads (Pure)


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
Issue number9
Early online date21 Jun 2017
Publication statusPublished - Jun 2017

Bibliographical note

APo and EU wish to acknowledge the Advanced Study Group activity at the Max Planck Institute for the Physics of Complex Systems in Dresden “From Microscopic to Collective Dynamics in Neural Circuits” for the opportunity to develop part of the project.


Dive into the research topics of 'Chaotic macroscopic phases in one-dimensional oscillators'. Together they form a unique fingerprint.

Cite this