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

By computing the Karhunen-Loeve decomposition (KLD) correlation length xi(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(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.