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arXiv · 0903.2236

Exponential localization of singular vectors in spatiotemporal chaos

Diego Pazó·Juan M. López·Miguel A. Rodríguez
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Abstract

In 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 improving existing forecasting techniques.

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Diego Pazó, Juan M. López, Miguel A. Rodríguez. 2009-03-12. Exponential localization of singular vectors in spatiotemporal chaos. https://doi.org/10.1103/physreve.79.036202

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