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Related Experiment Video

Updated: Feb 10, 2026

Predicting Amputation using Local Circulating Mononuclear Progenitor Cells in Angioplasty-treated Patients with Critical Limb Ischemia
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Bak-Sneppen model: Local equilibrium and critical value.

Daniel Fraiman1

  • 1Departamento de Matemática y Ciencias, Universidad de San Andrés, 1644 Buenos Aires, Argentina, and CONICET, Argentina.

Physical Review. E
|May 16, 2018
PubMed
Summary

The Bak-Sneppen model

Area of Science:

  • Complex systems
  • Statistical physics

Background:

  • The Bak-Sneppen (BS) model is a fundamental model in self-organized criticality.
  • Its critical value (p_c) and determining factors remain largely unknown.
  • The model's behavior at the thermodynamic limit involves uniform fitness distribution.

Purpose of the Study:

  • Investigate the Bak-Sneppen model with a focus on the lowest fitness particle.
  • Analyze the impact of interactions with an even number (m) of nearest neighbors.
  • Determine bounds for the critical value p_c and explore model transformations.

Main Methods:

  • Studied the BS model with m nearest neighbors for the lowest fitness particle.
  • Derived a local equilibrium relation for p_c.
  • Analyzed transformations preserving the model's complex dynamics.

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Main Results:

  • Established a local equilibrium relation for the critical value p_c.
  • Determined bounds for p_c in the BS model.
  • Obtained exact results for certain BS-like models.

Conclusions:

  • The local equilibrium relation provides a method to understand p_c.
  • Bounds for p_c offer new insights into the Bak-Sneppen model.
  • Model transformations can be performed without disrupting complex dynamics.