Extremal dynamics on complex networks: Analytic solutions

N. Masuda, Kwang-Il Goh, B. Kahng

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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
Volume72
Issue number6
DOIs
Publication statusPublished - 2005 Dec 1
Externally publishedYes

Fingerprint

Analytic Solution
Complex Networks
thresholds
Bak-Sneppen Model
biological evolution
Biological Evolution
fitness
Rate Equations
Random Networks
data simulation
Avalanche
Degree Distribution
Thermodynamic Limit
mutations
Critical Behavior
random walk
avalanches
Fitness
Updating
Random walk

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Extremal dynamics on complex networks : Analytic solutions. / Masuda, N.; Goh, Kwang-Il; Kahng, B.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 72, No. 6, 066106, 01.12.2005.

Research output: Contribution to journalArticle

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