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Exponential localization of singular vectors in spatiotemporal chaos

Journal: Physical Review E
Year: 2009   Volume: 79
Initial page: 36202  
Status: Published
In this status since: 11 Mar 2009
PDF file: 2009_pazo_pre.pdf
DOI: 10.1103/PhysRevE.79.036202
Pazó, D., López, J.M.,

In a dynamical system the singular vector SV indicates which perturbation will exhibit maximal growth after a time interval . 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 − for the localization of the SV. Moreover the same exponent  characterizes the finite- deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improve existing forecasting techniques.