Extremal dynamics on complex networks: Analytic solutions

N. Masuda, K. I. Goh, B. Kahng

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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(+1), where f=k2k (=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 γ<3 (γ>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)∼s-32.

Original languageEnglish
Article number066106
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
Publication statusPublished - 2005 Dec
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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