Universality Class of Bak-Sneppen Model on Scale-Free Network

We study the critical properties of the Bak-Sneppen coevolution model on scalefree networks by Monte Carlo method. We report the distribution of the avalanche size and fractal activity through the branching process. We observe that the critical fitness fc(N) depends on the number of the node such as fc(N) ∼ 1/ log(N) for both the scale-free network and the directed scale-free network. Near the critical fitness many physical quantities show power-law behaviors. The probability distribution P (s) of the avalanche size at the critical fitness shows a power-law like P (s) ∼ s−τ with τ = 1.80(3) regardless of the scale-free network and the directed scale free network. The probability distribution Pf (t) of the first return time also shows a power-law such as Pf (t) ∼ t −τf . The probability distribution of the first return time has two scaling regimes. The critical exponents τf are equivalent for both the scale-free network and the directed scale-free network. We obtain the critical exponents as τf1 = 2.7(1) at t < tc and τf2 = 1.72(3) at t > tc where the crossover time tc ∼ 100. The Bak-Sneppen model on the scale-free network and directed scalefree network shows a unique universality class. The critical exponents are different from the mean-field results. The directionality of the network does not change the universality on the network.