### 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 language | English |
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Article number | 066106 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 72 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2005 Dec 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*72*(6), [066106]. https://doi.org/10.1103/PhysRevE.72.066106

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

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 72, no. 6, 066106. https://doi.org/10.1103/PhysRevE.72.066106

}

TY - JOUR

T1 - Extremal dynamics on complex networks

T2 - Analytic solutions

AU - Masuda, N.

AU - Goh, Kwang-Il

AU - Kahng, B.

PY - 2005/12/1

Y1 - 2005/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=28844506361&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28844506361&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.72.066106

DO - 10.1103/PhysRevE.72.066106

M3 - Article

AN - SCOPUS:28844506361

VL - 72

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 066106

ER -