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Linear and nonlinear information flow in spatially extended systems.

M Cencini1, A Torcini

  • 1Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
Summary

Error propagation in extended systems depends on whether linear or nonlinear mechanisms dominate. Nonlinear effects can cause finite amplitude errors to travel faster than infinitesimal ones, impacting information transport.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Information Theory

Background:

  • Information transport in spatially extended systems is crucial for understanding complex phenomena.
  • Error propagation dynamics can be linear or nonlinear, affecting system behavior.
  • Distinguishing between linear and nonlinear error propagation is key to characterizing information flow.

Purpose of the Study:

  • To investigate infinitesimal and finite amplitude error propagation in spatially extended systems.
  • To characterize information transport using perturbation propagation velocity (Vp).
  • To differentiate between linear and nonlinear error propagation mechanisms.

Main Methods:

  • Linear stability analysis to determine infinitesimal error propagation velocity (VL).

Related Experiment Videos

  • Numerical and theoretical investigation of finite amplitude disturbances.
  • Application of the finite size Lyapunov exponent (FSLE) and its generalization.

    • Main Results:

    • Linear stability analysis accurately captures infinitesimal error propagation (Vp=VL) when linear mechanisms dominate.
    • Nonlinear mechanisms can lead to finite amplitude disturbances propagating faster than infinitesimal ones (Vp>VL).
    • The generalized FSLE provides a marginal stability criterion for Vp in both linear and nonlinear regimes.

    Conclusions:

    • The study reveals strong analogies between information spreading and reaction-diffusion front propagation.
    • Linear and nonlinear mechanisms play distinct roles in information flow within extended systems.
    • The findings enhance understanding of information dynamics in complex systems through a unified approach.