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.

Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach

“…In case of extended systems involving many degrees of freedom, there have been interesting studies concerning not only growth of small localized initial separation but also their spread in space. Examples include, propagation of chaos in reaction-diffusion systems [22,23], coupled-map lattices [24,25], Fermi-Pasta-Ulam (FPU) chain [26,27], complex Ginzburg-Landau system and the Gray-Scott network [28], where both Lyapunov exponents and spatial propagation of perturbation are discussed in the contexts of computing time delayed mutual information and redundancy [22], defining both temporal as well as spatial Lyapunov exponents [24], introducing entropy potential [25], convective Lyapunov spectrum [26] etc.…”

Length scale of a chaotic element in Rayleigh-Bénard convection

“…However, a similar depth of understanding of spatiotemporal chaos is lacking. A question of particular interest is the identification of appropriate length scales that describe and provide insight into spatiotemporal chaos [2][3][4][5][6][7].…”