Karhunen-Lo`eve Decomposition of Extensive Chaos

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Zoldi, SM; Greenside, HS

Digital Object Identifier (DOI)

  • 10.1103/PhysRevLett.78.1687