Extremal dynamics on complex networks: Analytic solutions

Details Extremal dynamics on complex networks: Analytic solutions Extremal dynamics on complex networks: Analytic solutions

2005-08-26

arxiv.org/abs/cond-mat/0508623v1

Phys. Rev. E 72, 066106 (2005).

Physics

Condensed Matter

Statistical Mechanics

6 pages, 2 figures

Scientific paper

10.1103/PhysRevE.72.066106

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 $x_c$ to be 1/(_f+1), where _f=/ (=) in the quenched (annealed) updating case, where is the n-th 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 x_c 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, P_a(s) ~ s^{-3/2}.

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