Hyperbolicity and the effective dimension of spatially extended dissipative systems

Hong-liu Yang, Kazumasa A. Takeuchi, Francesco Ginelli, Hugues Chate, Guenter Radons

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

Using covariant Lyapunov vectors, we reveal a split of the tangent space of standard models of one-dimensional dissipative spatiotemporal chaos: A finite extensive set of N dynamically entangled vectors with frequent common tangencies describes all of the physically relevant dynamics and is hyperbolically separated from possibly infinitely many isolated modes representing trivial, exponentially decaying perturbations. We argue that N can be interpreted as the number of effective degrees of freedom, which has to be taken into account in numerical integration and control issues.

Original languageEnglish
Article number074102
Number of pages4
JournalPhysical Review Letters
Volume102
Issue number7
DOIs
Publication statusPublished - 20 Feb 2009

Keywords

  • Ginzburg-Landau equation
  • chaos
  • exponents

Cite this

Hyperbolicity and the effective dimension of spatially extended dissipative systems. / Yang, Hong-liu; Takeuchi, Kazumasa A.; Ginelli, Francesco; Chate, Hugues; Radons, Guenter.

In: Physical Review Letters, Vol. 102, No. 7, 074102, 20.02.2009.

Research output: Contribution to journalArticle

Yang, Hong-liu ; Takeuchi, Kazumasa A. ; Ginelli, Francesco ; Chate, Hugues ; Radons, Guenter. / Hyperbolicity and the effective dimension of spatially extended dissipative systems. In: Physical Review Letters. 2009 ; Vol. 102, No. 7.
@article{f44ba6ee816c4860ac5a62688cb00d21,
title = "Hyperbolicity and the effective dimension of spatially extended dissipative systems",
abstract = "Using covariant Lyapunov vectors, we reveal a split of the tangent space of standard models of one-dimensional dissipative spatiotemporal chaos: A finite extensive set of N dynamically entangled vectors with frequent common tangencies describes all of the physically relevant dynamics and is hyperbolically separated from possibly infinitely many isolated modes representing trivial, exponentially decaying perturbations. We argue that N can be interpreted as the number of effective degrees of freedom, which has to be taken into account in numerical integration and control issues.",
keywords = "Ginzburg-Landau equation, chaos, exponents",
author = "Hong-liu Yang and Takeuchi, {Kazumasa A.} and Francesco Ginelli and Hugues Chate and Guenter Radons",
year = "2009",
month = "2",
day = "20",
doi = "10.1103/PhysRevLett.102.074102",
language = "English",
volume = "102",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "7",

}

TY - JOUR

T1 - Hyperbolicity and the effective dimension of spatially extended dissipative systems

AU - Yang, Hong-liu

AU - Takeuchi, Kazumasa A.

AU - Ginelli, Francesco

AU - Chate, Hugues

AU - Radons, Guenter

PY - 2009/2/20

Y1 - 2009/2/20

N2 - Using covariant Lyapunov vectors, we reveal a split of the tangent space of standard models of one-dimensional dissipative spatiotemporal chaos: A finite extensive set of N dynamically entangled vectors with frequent common tangencies describes all of the physically relevant dynamics and is hyperbolically separated from possibly infinitely many isolated modes representing trivial, exponentially decaying perturbations. We argue that N can be interpreted as the number of effective degrees of freedom, which has to be taken into account in numerical integration and control issues.

AB - Using covariant Lyapunov vectors, we reveal a split of the tangent space of standard models of one-dimensional dissipative spatiotemporal chaos: A finite extensive set of N dynamically entangled vectors with frequent common tangencies describes all of the physically relevant dynamics and is hyperbolically separated from possibly infinitely many isolated modes representing trivial, exponentially decaying perturbations. We argue that N can be interpreted as the number of effective degrees of freedom, which has to be taken into account in numerical integration and control issues.

KW - Ginzburg-Landau equation

KW - chaos

KW - exponents

U2 - 10.1103/PhysRevLett.102.074102

DO - 10.1103/PhysRevLett.102.074102

M3 - Article

VL - 102

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 7

M1 - 074102

ER -