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Self-organized criticality in a nutshell.

J Nagler1, C Hauert, H G Schuster

  • 1Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität, Olshausenstrasse 40, 24118 Kiel, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study introduces a minimal model for self-organized criticality (SOC), revealing a power-law distribution of disturbance durations. The model simplifies SOC dynamics to a leveling process, offering new insights into critical phenomena.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Dynamical Systems

Background:

  • Self-organized criticality (SOC) describes complex systems that naturally evolve to a critical state without external tuning.
  • Understanding the universal properties of SOC is crucial for various fields, including physics, biology, and geophysics.
  • Analytical models are needed to elucidate the fundamental mechanisms underlying SOC phenomena.

Purpose of the Study:

  • To present a minimal, analytically solvable model that captures the essential features of self-organized criticality (SOC).
  • To derive and analyze the probability distribution of disturbance durations in the critical state.
  • To investigate the impact of system stabilization and deviation from criticality on avalanche behavior.

Main Methods:

Related Experiment Videos

  • Development of a minimal model described by a single integer variable.
  • Analytical derivation of the probability distribution for disturbance durations.
  • Comparison of model dynamics to Ehrenfest's flea model (leveling process).

    • Main Results:

    • The model analytically reproduces a scale-invariant, power-law distribution of disturbance durations, a hallmark of SOC.
    • Finite-size effects are shown to result in an exponential tail of the distribution.
    • Large avalanches are suppressed both when stabilizing the system in its critical state and when driving it away from criticality.

    Conclusions:

    • The minimal model provides a tractable framework for understanding SOC dynamics.
    • The derived power-law distribution and finite-size effects offer quantitative insights into critical phenomena.
    • SOC dynamics can be effectively reduced to a leveling process, simplifying the study of complex systems.