2008/01/01 by Sarah Hallerberg, Diego Pazó, J.M. López +3 · 3 citations
Computer Science · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Applied mathematics #Chaos control and synchronization #Computer science #Ecosystem dynamics and resilience #Fluid Dynamics and Turbulent Flows #Geometry #Growth rate #Law #Logarithm #Logarithmic growth #Lyapunov exponent #Lyapunov function #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Norm (philosophy) #Perturbation (astronomy) #Physics #Piecewise #Scaling #Statistical physics #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.81.066204
published in 研究紀要 81(10), 16-25 (American Physical Society) · 8 pages, 8 figures
openalex publication_date 2008/01/01 · arxiv created 2010/05/25 · arxiv updated 2010/06/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/04/28
Bred vectors are a type of finite perturbation used in prediction studies of atmospheric models that exhibit spatially extended chaos. We study the structure, spatial correlations, and the growth rates of logarithmic bred vectors (which are constructed by using a given norm). We find that, after a suitable transformation, logarithmic bred vectors are roughly piecewise copies of the leading Lyapunov vector. This fact allows us to deduce a scaling law for the bred vector growth rate as a function of its amplitude. In addition, we relate growth rates with the spectrum of Lyapunov exponents corresponding to the most expanding directions. We illustrate our results with simulations of the Lorenz 1996 model.