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Extremal dynamics on complex networks: analytic solutions.

N Masuda1, K-I Goh, B Kahng

  • 1Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
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The Bak-Bak-Sneppen model on complex networks reveals punctuated equilibria. Its fitness threshold depends on network structure, with critical behavior observed in avalanche size distributions.

Area of Science:

  • Evolutionary biology
  • Complex systems
  • Network science

Background:

  • The Bak-Bak-Sneppen model simulates punctuated equilibria in evolution.
  • Understanding evolutionary dynamics on complex networks is crucial.

Purpose of the Study:

  • To analyze the Bak-Bak-Sneppen model on random complex networks.
  • To derive the fitness threshold and study avalanche size distributions.

Main Methods:

  • Analytical solutions using rate equation and random walk approaches.
  • Numerical simulations for validation.

Main Results:

  • Derived fitness threshold xc = 1/((k)f+1), dependent on degree distribution moments.
  • Identified threshold behavior (zero or finite) based on degree exponent gamma.

Related Experiment Videos

  • Observed power-law distribution for avalanche size (Pa(s) ~ s(-3/2)).
  • Theoretical predictions align with simulations in the annealed case.

    • Conclusions:

    • Network topology significantly influences evolutionary thresholds.
    • Avalanche size distribution indicates critical evolutionary dynamics.
    • The model provides insights into punctuated equilibria on evolving networks.