Karhunen-Loève local characterization of spatiotemporal chaos in a reaction-diffusion system

By computing the Karhunen-Loève decomposition (KLD) correlation length ${\xi }_{\mathrm{KLD}}$ of a reaction-diffusion system in the extensive chaos regime, we show that it is a sensitive measure of spatial dynamical inhomogeneities. It reveals substantial spatial nonuniformity of the dynamics at the boundaries and can also detect slow spatial variations in system parameters. The intensive length ${\xi }_{\mathrm{KLD}}$ can be easily computed from small local subsystems and is found to have a similar parametric dependence as the two-point correlation length computed over the full system size.