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Coevolutionary dynamics on scale-free networks.

Sungmin Lee1, Yup Kim

  • 1Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
Summary

This study explores Bak-Sneppen coevolution models on scale-free networks. Critical fitness values and avalanche distributions differ significantly based on the network

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Area of Science:

  • Complex Systems
  • Network Science
  • Statistical Physics

Background:

  • Bak-Sneppen models simulate coevolutionary dynamics.
  • Scale-free networks are prevalent in natural and artificial systems.
  • Network topology significantly influences system behavior.

Purpose of the Study:

  • Investigate Bak-Sneppen coevolution models on scale-free networks with varying degree exponents (gamma).
  • Analyze the impact of network structure on critical fitness values and avalanche size distributions.
  • Explain the observed phenomena analytically.

Main Methods:

  • Simulations of Bak-Sneppen coevolution models on scale-free networks.
  • Analytical derivation of critical fitness values as a function of network size (N) and average degree.
  • Analysis of avalanche size distribution (P(s)) for different degree exponents.

Main Results:

  • For gamma > 3, critical fitness (f(c)) approaches a finite, non-zero value, and avalanche distributions follow normal power laws.
  • For 2 < gamma <= 3, f(c) approaches zero, and avalanche distributions exhibit two power-law regimes (tau(1) > tau(2)).
  • Analytical formula f(c)(N) ≈ A/<(k+1)^2>(N) explains the critical fitness behavior.

Conclusions:

  • Network degree exponent critically determines the behavior of Bak-Sneppen models.
  • The emergence of two power-law regimes in avalanche distributions for 2 < gamma <= 3 is linked to star-like network dynamics.
  • Understanding these coevolutionary dynamics is crucial for complex network analysis.

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