### 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