Lyapunov analysis captures the collective dynamics of large chaotic systems

Kazumasa A. Takeuchi, Francesco Ginelli, Hugues Chate

Research output: Contribution to journalArticle

27 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

Cite this

Lyapunov analysis captures the collective dynamics of large chaotic systems. / Takeuchi, Kazumasa A.; Ginelli, Francesco; Chate, Hugues.

In: Physical Review Letters, Vol. 103, No. 15, 154103, 09.10.2009.

Research output: Contribution to journalArticle

Takeuchi, Kazumasa A. ; Ginelli, Francesco ; Chate, Hugues. / Lyapunov analysis captures the collective dynamics of large chaotic systems. In: Physical Review Letters. 2009 ; Vol. 103, No. 15.
@article{2bfae270dd6c4a1ea3b0ae1197269cef,
title = "Lyapunov analysis captures the collective dynamics of large chaotic systems",
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 = "globally coupled maps, characteristic exponents, large numbers, limit, oscillators, law",
author = "Takeuchi, {Kazumasa A.} and Francesco Ginelli and Hugues Chate",
year = "2009",
month = "10",
day = "9",
doi = "10.1103/PhysRevLett.103.154103",
language = "English",
volume = "103",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "15",

}

TY - JOUR

T1 - Lyapunov analysis captures the collective dynamics of large chaotic systems

AU - Takeuchi, Kazumasa A.

AU - Ginelli, Francesco

AU - Chate, Hugues

PY - 2009/10/9

Y1 - 2009/10/9

N2 - 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.

AB - 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.

KW - globally coupled maps

KW - characteristic exponents

KW - large numbers

KW - limit

KW - oscillators

KW - law

U2 - 10.1103/PhysRevLett.103.154103

DO - 10.1103/PhysRevLett.103.154103

M3 - Article

VL - 103

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 15

M1 - 154103

ER -