Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices

Abstract

The spatiotemporal dynamics of Lyapunov vectors (LVs) in spatially extended chaotic systems is studied by means of coupled-map lattices. We determine intrinsic length scales and spatiotemporal correlations of LVs corresponding to the leading unstable directions by translating the problem to the language of scale-invariant growing surfaces. We find that the so-called 'characteristic' LVs exhibit spatial localization, strong clustering around given spatiotemporal loci, and remarkable dynamic scaling properties of the corresponding surfaces. In contrast, the commonly used backward LVs (obtained through Gram-Schmidt orthogonalization) spread all over the system and do not exhibit dynamic scaling due to artifacts in the dynamical correlations by construction.

References in corpus (3)

• Scaling properties of growing noninfinitesimal perturbations in space-time chaos
• Universality classes of the Kardar-Parisi-Zhang equation
• Rare Events and Scale--Invariant Dynamics of Perturbations in Delayed Dynamical Systems

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• Initial perturbation matters: implications of geometry-dependent universal Kardar-Parisi-Zhang statistics for spatiotemporal chaos
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