Lyapunov analysis captures the collective dynamics of large chaotic systems

Kazumasa A. Takeuchi, Francesco Ginelli, Hugues Chate

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29 Citations (Scopus)

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.

Original languageEnglish
Article number154103
Number of pages4
JournalPhysical Review Letters
Volume103
Issue number15
DOIs
Publication statusPublished - 9 Oct 2009

Keywords

  • globally coupled maps
  • characteristic exponents
  • large numbers
  • limit
  • oscillators
  • law

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