Extremal dynamics on complex networks: analytic solutions.

@article{Masuda2005ExtremalDO,
title={Extremal dynamics on complex networks: analytic solutions.},
author={Naoki Masuda and K I Goh and B. Kahng},
journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
year={2005},
volume={72 6 Pt 2},
pages={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 xc to be 1/((k)f+1), where (k)f=(k2)/(k) (=(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 gamma<3 (gamma>3) for the quenched case in the… CONTINUE READING