English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Universal finite-sample effect on the perturbation growth in chaotic dynamical systems

MPS-Authors
/persons/resource/persons21881

Mikhailov,  Alexander S.
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

e026213.pdf
(Publisher version), 700KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Nakao, H., Kitada, S., & Mikhailov, A. S. (2006). Universal finite-sample effect on the perturbation growth in chaotic dynamical systems. Physical Review E, 74(2): 026213. doi:10.1103/PhysRevE.74.026213.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-03B8-2
Abstract
The finite-sample effect on the growth of moments of the perturbation observed in numerical simulations of chaotic dynamical systems is studied. To numerically estimate the moments, only a limited number of sample trajectories can be utilized, and therefore the moments exhibit pure exponential growth only initially, and give way to relaxed growth thereafter. Such transition is a consequence of the unobservability of rare events in finite sample sets. Using the large-deviation formalism for chaotic time series, we estimate the relaxation time and derive the post-relaxation growth law. We demonstrate that even after the relaxation, each moment still obeys a universal growth law of different type, which reflects physical information on the statistics of chaotic expansion rates.