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Title

Exponential localization of singular vectors in spatiotemporal chaos

AuthorsPazó, Diego CSIC ORCID ; López, Juan M. CSIC ORCID ; Rodríguez, Miguel A. CSIC ORCID
KeywordsChaos
Lyapunov methods
Nonlinear dynamical systems
Spatiotemporal phenomena
Vectors
High-dimensional chaos
Fluctuation phenomena
Weather analysis and prediction
Issue Date11-Mar-2009
PublisherAmerican Physical Society
CitationPhysical Review E 79(3): 036202 (2009)
AbstractIn a dynamical system the singular vector (SV) indicates which perturbation will exhibit maximal growth after a time interval τ. We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a suitable transformation, the SV can be described in terms of the Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us to deduce a universal power law τ(−γ) for the localization of the SV. Moreover the same exponent γ characterizes the finite-τ deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improve existing forecasting techniques.
Description5 pages, 4 figures.-- PACS nrs.: 05.45.Jn; 05.40.-a; 05.45.Ra; 92.60.Wc.
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevE.79.036202
URIhttp://hdl.handle.net/10261/11517
DOI10.1103/PhysRevE.79.036202
ISSN1539-3755
Appears in Collections:(IFCA) Artículos

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