Karhunen-Lo`eve Decomposition of Extensive Chaos

Details Karhunen-Lo`eve Decomposition of Extensive Chaos Karhunen-Lo`eve Decomposition of Extensive Chaos

1996-10-02

arxiv.org/abs/chao-dyn/9610007v1

Nonlinear Sciences

Chaotic Dynamics

12 pages including 4 figures, uses REVTeX macros. To appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.78.1687

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.

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