Karhunen-Lo`eve Decomposition of Extensive Chaos
Abstract
We show that the number of KLD (Karhunen-Lo`eve decomposition) modes DKLD(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 xiKLD(f) to be defined that is easily calculated from spatially localized data. We show that xiKLD(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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