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Linear and nonlinear information flow in spatially extended systems

Massimo Cencini

Alessandro Torcini

  • Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany

  • Physics Department, Università “La Sapienza,” piazzale Aldo Moro 2, I-00185 Roma, Italy
  • Istituto Nazionale di Fisica della Materia, UdR Firenze, L.go E. Fermi, 3 I-50125 Firenze, Italy

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Phys. Rev. E 63, 056201 – Published 11 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.056201

Abstract

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.

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Phys. Rev. E 63, 056201– Published 11 April, 2001
  • Received 23 November 2000

© 2001 American Physical Society

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