Finite size Lyapunov exponent at a saddle point

A simple stochastic system is considered modeling Lagrangian motion in a vicinity of a hyperbolic stationary point in two dimensions. We address the dependence of the Finite Size Lyapunov Exponent (FSLE) λ on the diffusivity D and the direction of the initial separation θ. It is shown that there is...

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Bibliographic Details
Published in:Applied mathematical modelling 2015-08, Vol.39 (15), p.4523-4533
Main Author: Piterbarg, Leonid I.
Format: Article
Language:English
Subjects:
FSLE
Hyperbolic stochastic system
Saddle point
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Summary:A simple stochastic system is considered modeling Lagrangian motion in a vicinity of a hyperbolic stationary point in two dimensions. We address the dependence of the Finite Size Lyapunov Exponent (FSLE) λ on the diffusivity D and the direction of the initial separation θ. It is shown that there is an insignificant difference between the curves λ=λ(θ) for pure dynamics (D=0) and for infinitely large noise (D=∞). For small D a well known boundary layer asymptotic is employed and compared with numerical results.
ISSN:0307-904X
DOI:10.1016/j.apm.2015.01.002