2000/11/30 by Massimo Cencini, Alessandro Torcini · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Computer science #Exponent #Flow (mathematics) #Generalization #Geometry #Infinitesimal #Linear stability #Linear system #Lyapunov exponent #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Spectroscopy and Quantum Chemical Studies #Stability (learning theory) #Statistical physics #cond-mat #math-ph #math.MP #nlin.CD #nlin.PS #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.63.056201
published as Physical Review E 63, 056201 (2001) · 14 RevTeX pages with 13 eps figures, title/abstract changed minor changes in the text accepted for publication on PRE
arxiv created 2001/01/19 · openalex publication_date 2001/04/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information transport in these systems can be characterized in terms of the propagation velocity of perturbations Vp. A linear stability analysis is sufficient to capture all the relevant aspects associated to propagation of infinitesimal disturbances. In particular, this analysis gives the propagation velocity VL of infinitesimal errors. If linear mechanisms prevail on the nonlinear ones Vp=VL. On the contrary, if nonlinear effects are predominant finite amplitude disturbances can eventually propagate faster than infinitesimal ones (i.e., Vp>VL). The finite size Lyapunov exponent can be successfully employed to discriminate the linear or nonlinear origin of information flow. A generalization of the finite size Lyapunov exponent to a comoving reference frame allows us to state a marginal stability criterion able to provide Vp both in the linear and in the nonlinear case. Strong analogies are found between information spreading and propagation of fronts connecting steady states in reaction-diffusion systems. The analysis of the common characteristics of these two phenomena leads to a better understanding of the role played by linear and nonlinear mechanisms for the flow of information in spatially extended systems.