Length scale of interaction in spatiotemporal chaos

Abstract

Extensive systems have no long scale correlations and behave as a sum of their parts. Various techniques are introduced to determine a characteristic length scale of interaction beyond which spatiotemporal chaos is extensive in reaction-diffusion networks. Information about network size, boundary condition, or abnormalities in network topology gets scrambled in spatiotemporal chaos, and the attenuation of information provides such characteristic length scales. Space-time information flow associated with the recovery of spatiotemporal chaos from finite perturbations, a concept somewhat opposite to the paradigm of Lyapunov exponents, defines another characteristic length scale. High-precision computational studies of asymptotic spatiotemporal chaos in the complex Ginzburg-Landau system and transient spatiotemporal chaos in the Gray-Scott network show that these different length scales are comparable and thus suitable to define a length scale of interaction. Preliminary studies demonstrate the relevance of these length scales for stable chaos.