Hyperbolicity and the Effective Dimension of Spatially Extended Dissipative Systems

Hong-liu Yang, Kazumasa A. Takeuchi, Francesco Ginelli, Hugues Chaté, and Günter Radons
Phys. Rev. Lett. 102, 074102 – Published 18 February 2009

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.

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  • Received 31 July 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.074102

©2009 American Physical Society

Authors & Affiliations

Hong-liu Yang1, Kazumasa A. Takeuchi2,3, Francesco Ginelli2,4, Hugues Chaté2, and Günter Radons1

  • 1Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
  • 2CEA - Service de Physique de l’État Condensé, CEN Saclay, 91191 Gif-sur-Yvette, France
  • 3Department of Physics, The University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
  • 4Institut des Systèmes Complexes de Paris Ile-de-France, 57-59 Rue Lhomond, 75005 Paris, France

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Issue

Vol. 102, Iss. 7 — 20 February 2009

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