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Self-organized critical random Boolean networks.

B Luque1, F J Ballesteros, E M Muro

  • 1Centro de Astrobiología INTA-CSIC, Carretera de Ajalvir km. 4, 28850 Torrejón de Ardoz, Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
Summary
This summary is machine-generated.

Standard Boolean networks exhibit phase transitions. Adding a disconnection rule drives these networks to a critical state, revealing self-organized criticality under perturbations, confirmed by simulations and analysis.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Network theory

Background:

  • Standard random Boolean networks (RBNs) are models for complex systems.
  • RBNs are known to exhibit a phase transition between ordered and disordered states.

Purpose of the Study:

  • To investigate the effect of a disconnection rule on RBNs.
  • To drive RBNs to a critical state and explore self-organized criticality.

Main Methods:

  • Introduction of a disconnection rule coupling control and order parameters in RBNs.
  • Numerical simulations to observe system behavior.
  • Comparison of simulation results with analytical treatment.

Main Results:

  • The disconnection rule successfully drives the RBN system to the critical line transition.
  • The system exhibits self-organized critical behavior when subjected to perturbations.
  • Numerical simulations align with the proposed analytical model.

Conclusions:

  • A novel disconnection rule can steer RBNs to criticality.
  • RBNs can display self-organized criticality, a significant finding for complex systems.
  • The study provides a validated analytical framework for understanding these critical dynamics.