Karhunen-Lo`eve Decomposition of Extensive Chaos
chao-dyn
2009-10-28 v1 Chaotic Dynamics
Abstract
We show that the number of KLD (Karhunen-Lo`eve decomposition) modes D_KLD(f) needed to capture a fraction f of the total variance of an extensively chaotic state scales extensively with subsystem volume V. This allows a correlation length xi_KLD(f) to be defined that is easily calculated from spatially localized data. We show that xi_KLD(f) has a parametric dependence similar to that of the dimension correlation length and demonstrate that this length can be used to characterize high-dimensional inhomogeneous spatiotemporal chaos.
Keywords
Cite
@article{arxiv.chao-dyn/9610007,
title = {Karhunen-Lo`eve Decomposition of Extensive Chaos},
author = {Scott M. Zoldi and Henry S. Greenside},
journal= {arXiv preprint arXiv:chao-dyn/9610007},
year = {2009}
}
Comments
12 pages including 4 figures, uses REVTeX macros. To appear in Phys. Rev. Lett