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.
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Politi, A., Pikovsky, A. & Ullner, E. Chaotic macroscopic phases in one-dimensional oscillators. Eur. Phys. J. Spec. Top. 226, 1791–1810 (2017). https://doi.org/10.1140/epjst/e2017-70056-4
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DOI: https://doi.org/10.1140/epjst/e2017-70056-4