Coevolutionary dynamics on scale-free networks

We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents g including random networks. For g. 3, the critical fitness value f(c) approaches a nonzero finite value in the limit N ->infinity, whereas f(c) approaches zero as 2 < gamma <= 3. These results are explained by showing analytically f(c)(N). similar or equal to A/<(k+1)(2)>(N) on the networks with size N. The avalanche size distribution P(s) shows the normal power-law behavior for gamma > 3. In contrast, P(s) for 2 < gamma <= 3 has two power-law regimes. One is a short regime for small s with a large exponent tau(1) and the other is a long regime for large s with a small exponent tau(2) (tau(1) > tau(2)). The origin of the two power regimes is explained by the dynamics on an artificially made star-linked network.