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Stability of the Kauffman model.

Sven Bilke1, Fredrik Sjunnesson

  • 1Complex Systems Division, Department of Theoretical Physics, University of Lund, Sölvegatan 14A, S-223 62 Lund, Sweden. sven@thep.lu.se

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
Summary

A novel decimation algorithm reveals a "stable core" in Random Boolean networks (Kauffman model). This core

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Area of Science:

  • Complex systems
  • Computational biology
  • Network theory

Background:

  • Random Boolean networks (Kauffman model) are widely used to model gene regulatory networks.
  • Understanding their dynamics, attractors, and sensitivity to perturbations is crucial.
  • Previous studies suggested insensitivity to perturbations and a specific growth rate for limit cycles.

Purpose of the Study:

  • To develop a novel decimation algorithm for analyzing Random Boolean networks.
  • To identify and characterize the 'stable core' of these networks.
  • To investigate the sensitivity of attractors and the growth of limit cycles in large networks.

Main Methods:

  • A novel decimation algorithm was developed to remove irrelevant variables from Random Boolean networks.
  • The algorithm identifies a 'stable core' comprising variables with fixed states in limit cycles.
  • Full enumeration studies were performed for networks up to N=32 to analyze limit cycle growth.

Main Results:

  • The stable core's size grows approximately linearly with the network size (N).
  • Reduced networks exhibit increased sensitivity to perturbations, unlike full Kauffman networks.
  • The number of limit cycles in critical Kauffman networks shows strong evidence of linear growth with N, contrasting previous theories.

Conclusions:

  • The stable core's dynamics are responsible for the insensitivity to perturbations observed in full Kauffman networks.
  • The decimation algorithm provides a new tool for analyzing large-scale complex networks.
  • The linear growth of limit cycles challenges existing models and suggests new directions for research in Boolean network dynamics.

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