Computing covariant Lyapunov vectors, Oseledets vectors, and dichotomy projectors: A comparative numerical study

PHYSICA D-NONLINEAR PHENOMENA

卷:247

Article

Froyland, Gary¹  Huels, Thorsten²  Morriss, Gary P.³  Watson, Thomas M.¹ 

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

[3] Univ New S Wales, Sch Phys, Sydney, NSW 2052, Australia

关键词: Covariant Lyapunov vectors;    Oseledets vectors;    Sacker-Sell spectrum;    Multiplicative Ergodic Theorem;    Lyapunov exponents;    Dichotomy projectors;   

DOI  :  10.1016/j.physd.2012.12.005

来源: Elsevier

【 摘 要 】

Covariant Lyapunov vectors or Oseledets vectors are increasingly being used for a variety of model analyses in areas such as partial differential equations, nonautonomous differentiable dynamical systems, and random dynamical systems. These vectors identify spatially varying directions of specific asymptotic growth rates and obey equivariance principles. In recent years new computational methods for approximating Oseledets vectors have been developed, motivated by increasing model complexity and greater demands for accuracy. In this numerical study we introduce two new approaches based on singular value decomposition and exponential dichotomies and comparatively review and improve two recent popular approaches of Ginelli et al. (2007) [36] and Wolfe and Samelson (2007) [37]. We compare the performance of the four approaches via three case studies with very different dynamics in terms of symmetry, spectral separation, and dimension. We also investigate which methods perform well with limited data. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free