Coevolutionary dynamics on scale-free networks.

We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents gamma including random networks. For gamma>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< or =3. These results are explained by showing analytically f(c) (N) approximately =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 < or =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.