Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices

Details Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices

2007-06-12

arxiv.org/abs/0706.1706v2

Phys. Rev. E 76, 025202 (2007)

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevE.76.025202

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.

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