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arXiv · 0907.4298

Lyapunov analysis captures the collective dynamics of large chaotic systems

Kazumasa A. Takeuchi·Francesco Ginelli·Hugues Chaté
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Abstract

We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting collectively on the trajectory. For globally-coupled maps, we show moreover a quantitative correspondence between the collective modes and some of the so-called Perron-Frobenius dynamics. Our results imply that the conventional definition of extensivity must be changed as soon as collective dynamics sets in.

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Kazumasa A. Takeuchi, Francesco Ginelli, Hugues Chaté. 2009-10-11. Lyapunov analysis captures the collective dynamics of large chaotic systems. https://doi.org/10.1103/physrevlett.103.154103

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