Extremal dynamics on complex networks: analytic solutions.

The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold xc to be 1/((k)f+1), where (k)f=(k2)/(k) (=(k)) in the quenched (annealed) updating case, where kn is the nth moment of the degree distribution. Thus, the threshold is zero (finite) for the degree exponent gamma<3 (gamma>3) for the quenched case in the thermodynamic limit. The theoretical value xc fits well to the numerical simulation data in the annealed case only. Avalanche size, defined as the duration of successive mutations below the threshold, exhibits a critical behavior as its distribution follows a power law, Pa(s) approximately s(-3/2).

• Publication year

  2005

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2005-08-26

• Fields of study

  Biology, Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.72.066106arXiv cond-mat/0508623PMID 16486009
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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