Lyapunov analysis captures the collective dynamics of large chaotic systems
Chaotic Dynamics
2009-10-11 v2 Statistical Mechanics
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.
Keywords
Cite
@article{arxiv.0907.4298,
title = {Lyapunov analysis captures the collective dynamics of large chaotic systems},
author = {Kazumasa A. Takeuchi and Francesco Ginelli and Hugues Chaté},
journal= {arXiv preprint arXiv:0907.4298},
year = {2009}
}
Comments
4 pages, 4 figures; small changes, mostly stylistic, made in v2